Quadrilaterals - GMAT Quantitative
Card 0 of 712
What is the length of the diagonal of rectangle 
?
(1) 
(2) 
and 
What is the length of the diagonal of rectangle
(1)
(2)
Tap to see back →
In order to find the diagonal, we must know the sides of the rectangle or know whether the triangles ADC or ABD have special angles.
Statement 1 alone doesn't let us calculate the hypothenuse of the triangles, because we only know one side.
Statement 2 alone is sufficient because it allows us to find all angles of the triangles inside of the rectangle. We can see that they are special triangles with angles 30-60-90. Any triangle with these angles will have its sides in ratio 
, where 
is a constant. Here, 
, knowing this, we can calculate the length of the hypothenuse, also the diagonal, which will be 
.
Hence, statement 2 is sufficient.
In order to find the diagonal, we must know the sides of the rectangle or know whether the triangles ADC or ABD have special angles.
Statement 1 alone doesn't let us calculate the hypothenuse of the triangles, because we only know one side.
Statement 2 alone is sufficient because it allows us to find all angles of the triangles inside of the rectangle. We can see that they are special triangles with angles 30-60-90. Any triangle with these angles will have its sides in ratio
Hence, statement 2 is sufficient.
Rectangle 
has a perimeter of 
, what is its area?
I) The diagonal of 
is 
inches.
II) The length of one side is 
inches.
Rectangle
I) The diagonal of
II) The length of one side is
Tap to see back →
I) Gives us the length of ASOF's diagonal. This by itself does not give us any way of finding the other sides.
II) Gives us one side length. From there we can use the perimeter to find the other side length and then the area.
Therefore, Statement II is sufficient to answer the question.
I) Gives us the length of ASOF's diagonal. This by itself does not give us any way of finding the other sides.
II) Gives us one side length. From there we can use the perimeter to find the other side length and then the area.
Therefore, Statement II is sufficient to answer the question.
Rectangle 
, has diagonal 
. What is the length of 
?
(1) Angle 
.
(2) 
.
Rectangle
(1) Angle
(2)
Tap to see back →
The length of a diagonal of a rectangle can be calculated like a hypotenuse using the Pythagorean Theorem provided we have information about the lengths of the rectangle.
Statement 1 tells us that both triangles ADC and ABD have their angles in ratio 
, which means that their sides will have length in ratio 
, where 
is a constant. We can't tell however what length the diagonal will be.
Statment 2 tells us that side AC is 1. From there we can't conclude anything. Indeed, rectangle ABCD might as well be a square or a very thin rectangle, we don't know.
Both statements together however, allow us to tell that 
and therefore that the diagonal will be 2.
Hence, both statements together are sufficient.
The length of a diagonal of a rectangle can be calculated like a hypotenuse using the Pythagorean Theorem provided we have information about the lengths of the rectangle.
Statement 1 tells us that both triangles ADC and ABD have their angles in ratio
Statment 2 tells us that side AC is 1. From there we can't conclude anything. Indeed, rectangle ABCD might as well be a square or a very thin rectangle, we don't know.
Both statements together however, allow us to tell that
Hence, both statements together are sufficient.
is a rectangle. What is the ratio 
?
(1) 
.
(2) 
.
(1)
(2)
Tap to see back →
To solve this, we need information about the lengths of the sides or to whether triangles ADB and ACD are special triangles.
Statement 1 tells us that CDA has length 3. This is not enough and we still don't know whether the rectangle is of a special type of rectangle.
Statement 2 tells us that triangles ADB and ACD are special triangles, indeed, they have their angles in ratio 
. That means that their sides will be in ratio 
. Now we don't need to know what is constant 
, since it will cancel out in the ratio.
Therefore, statement 2 alone is sufficient.
To solve this, we need information about the lengths of the sides or to whether triangles ADB and ACD are special triangles.
Statement 1 tells us that CDA has length 3. This is not enough and we still don't know whether the rectangle is of a special type of rectangle.
Statement 2 tells us that triangles ADB and ACD are special triangles, indeed, they have their angles in ratio
Therefore, statement 2 alone is sufficient.
Find the diagonal of rectangle 
.
I) The area of 
is 
.
II) The perimeter of 
is 
.
Find the diagonal of rectangle
I) The area of
II) The perimeter of
Tap to see back →
In order to find the diagonal of a rectangle we need the length of both sides.
We can't find the lengths with just the area or just the perimeter, but by using them both together we can make a small system of equations with two unknowns and two equations.
Then we can solve for each side and use the Pythagorean Theorem to find our diagonal.
In order to find the diagonal of a rectangle we need the length of both sides.
We can't find the lengths with just the area or just the perimeter, but by using them both together we can make a small system of equations with two unknowns and two equations.
Then we can solve for each side and use the Pythagorean Theorem to find our diagonal.
What is the length of the diagonal of rectangle ?
(1)
(2) and
What is the length of the diagonal of rectangle
(1)
(2)
Tap to see back →
In order to find the diagonal, we must know the sides of the rectangle or know whether the triangles ADC or ABD have special angles.
Statement 1 alone doesn't let us calculate the hypothenuse of the triangles, because we only know one side.
Statement 2 alone is sufficient because it allows us to find all angles of the triangles inside of the rectangle. We can see that they are special triangles with angles 30-60-90. Any triangle with these angles will have its sides in ratio , where is a constant. Here, , knowing this, we can calculate the length of the hypothenuse, also the diagonal, which will be .
Hence, statement 2 is sufficient.
In order to find the diagonal, we must know the sides of the rectangle or know whether the triangles ADC or ABD have special angles.
Statement 1 alone doesn't let us calculate the hypothenuse of the triangles, because we only know one side.
Statement 2 alone is sufficient because it allows us to find all angles of the triangles inside of the rectangle. We can see that they are special triangles with angles 30-60-90. Any triangle with these angles will have its sides in ratio
Hence, statement 2 is sufficient.
Rectangle has a perimeter of , what is its area?
I) The diagonal of is inches.
II) The length of one side is inches.
Rectangle
I) The diagonal of
II) The length of one side is
Tap to see back →
I) Gives us the length of ASOF's diagonal. This by itself does not give us any way of finding the other sides.
II) Gives us one side length. From there we can use the perimeter to find the other side length and then the area.
Therefore, Statement II is sufficient to answer the question.
I) Gives us the length of ASOF's diagonal. This by itself does not give us any way of finding the other sides.
II) Gives us one side length. From there we can use the perimeter to find the other side length and then the area.
Therefore, Statement II is sufficient to answer the question.
Rectangle , has diagonal . What is the length of ?
(1) Angle .
(2) .
Rectangle
(1) Angle
(2)
Tap to see back →
The length of a diagonal of a rectangle can be calculated like a hypotenuse using the Pythagorean Theorem provided we have information about the lengths of the rectangle.
Statement 1 tells us that both triangles ADC and ABD have their angles in ratio , which means that their sides will have length in ratio , where is a constant. We can't tell however what length the diagonal will be.
Statment 2 tells us that side AC is 1. From there we can't conclude anything. Indeed, rectangle ABCD might as well be a square or a very thin rectangle, we don't know.
Both statements together however, allow us to tell that and therefore that the diagonal will be 2.
Hence, both statements together are sufficient.
The length of a diagonal of a rectangle can be calculated like a hypotenuse using the Pythagorean Theorem provided we have information about the lengths of the rectangle.
Statement 1 tells us that both triangles ADC and ABD have their angles in ratio
Statment 2 tells us that side AC is 1. From there we can't conclude anything. Indeed, rectangle ABCD might as well be a square or a very thin rectangle, we don't know.
Both statements together however, allow us to tell that
Hence, both statements together are sufficient.
is a rectangle. What is the ratio ?
(1) .
(2) .
(1)
(2)
Tap to see back →
To solve this, we need information about the lengths of the sides or to whether triangles ADB and ACD are special triangles.
Statement 1 tells us that CDA has length 3. This is not enough and we still don't know whether the rectangle is of a special type of rectangle.
Statement 2 tells us that triangles ADB and ACD are special triangles, indeed, they have their angles in ratio . That means that their sides will be in ratio . Now we don't need to know what is constant , since it will cancel out in the ratio.
Therefore, statement 2 alone is sufficient.
To solve this, we need information about the lengths of the sides or to whether triangles ADB and ACD are special triangles.
Statement 1 tells us that CDA has length 3. This is not enough and we still don't know whether the rectangle is of a special type of rectangle.
Statement 2 tells us that triangles ADB and ACD are special triangles, indeed, they have their angles in ratio
Therefore, statement 2 alone is sufficient.
Find the diagonal of rectangle .
I) The area of is .
II) The perimeter of is .
Find the diagonal of rectangle
I) The area of
II) The perimeter of
Tap to see back →
In order to find the diagonal of a rectangle we need the length of both sides.
We can't find the lengths with just the area or just the perimeter, but by using them both together we can make a small system of equations with two unknowns and two equations.
Then we can solve for each side and use the Pythagorean Theorem to find our diagonal.
In order to find the diagonal of a rectangle we need the length of both sides.
We can't find the lengths with just the area or just the perimeter, but by using them both together we can make a small system of equations with two unknowns and two equations.
Then we can solve for each side and use the Pythagorean Theorem to find our diagonal.
Find the length of the diagonal of square G.
I) The area of G is 
fathoms squared.
II) The side length of G is 
fathoms.
Find the length of the diagonal of square G.
I) The area of G is
II) The side length of G is
Tap to see back →
We can use the side length and the Pythagorean Theorem to find the diagonal of a square.
We can find side length from area, so we could solve this with either I or II.
We can use the side length and the Pythagorean Theorem to find the diagonal of a square.
We can find side length from area, so we could solve this with either I or II.
The circle with center 
is inscribed in square 
. What is the length of diagonal 
?
(1) The area of the circle is 
.
(2) The side of the square is 
.
The circle with center
(1) The area of the circle is
(2) The side of the square is
Tap to see back →
The diagonal of the square can be calculated as long as we have any information about the lengths or area of the circle or of the square.
Statement 1, by giving us the area of the circle, allows us to find the radius of the circle, which is half the length of the side. Therefore statement 1 alone is sufficient.
Statement 2, by telling us the length of a side of the square is also sufficient, and would allow us to calculate the length of the diagonal.
Therefore, each statement alone is sufficient.
The diagonal of the square can be calculated as long as we have any information about the lengths or area of the circle or of the square.
Statement 1, by giving us the area of the circle, allows us to find the radius of the circle, which is half the length of the side. Therefore statement 1 alone is sufficient.
Statement 2, by telling us the length of a side of the square is also sufficient, and would allow us to calculate the length of the diagonal.
Therefore, each statement alone is sufficient.
On your college campus there is a square grassy area where people like to hangout and enjoy the sun. While walking with some friends, you decide to take the shortest distance to the corner of the square opposite from where you are. Find the distance you traveled.
I) The perimeter of the square is 
meters.
II) The square covers an area of 
square meters.
On your college campus there is a square grassy area where people like to hangout and enjoy the sun. While walking with some friends, you decide to take the shortest distance to the corner of the square opposite from where you are. Find the distance you traveled.
I) The perimeter of the square is
II) The square covers an area of
Tap to see back →
We are asked to find the length of a diagonal of a square.
We can do this if we have the side length. We can find side length from either perimeter or area.
From Statement I)
In this case, our side length is 15 meters.
We can use this and Pythagorean Theorem or 45/45/90 triangles to find our diagonal.
From Statement II)
From here, we can plug the side length into the Pythagorean Theorem like before and solve for the diagonal.
Therefore, either statement alone is sufficient to answer the question.
We are asked to find the length of a diagonal of a square.
We can do this if we have the side length. We can find side length from either perimeter or area.
From Statement I)
In this case, our side length is 15 meters.
We can use this and Pythagorean Theorem or 45/45/90 triangles to find our diagonal.
From Statement II)
From here, we can plug the side length into the Pythagorean Theorem like before and solve for the diagonal.
Therefore, either statement alone is sufficient to answer the question.
What is the length of the diagonal of the square?
- The area of the square is
.
- The perimeter is
.
What is the length of the diagonal of the square?
- The area of the square is
- The perimeter is
Tap to see back →
The length of the diagonal of a square is given by 
, where 
represents the square's side. As such, we need the length of the square's side.
Statement 1: 
Statement 2: 
Both statements provide us with the length of the square's side.
The length of the diagonal of a square is given by
Statement 1:
Statement 2:
Both statements provide us with the length of the square's side.
Find the length of the diagonal of square A if the diagonal of square B is 
.
- The perimeter of square B is
- The area of square A is
Find the length of the diagonal of square A if the diagonal of square B is
- The perimeter of square B is
- The area of square A is
Tap to see back →
Statement 1: The information provided would only be useful if the ratio of square A to square B was known.
Statement 2: We need the length of the square's side to find the length of the diagonal and we can use the area to solve for the length of the side.
Now we can find the diagonal: 
Statement 1: The information provided would only be useful if the ratio of square A to square B was known.
Statement 2: We need the length of the square's side to find the length of the diagonal and we can use the area to solve for the length of the side.
Now we can find the diagonal:
The diagonal bracing of a square pallet measures 
. What is the area of the pallet?
The diagonal bracing of a square pallet measures
Tap to see back →
To solve this problem, we must recognize that the diagonal bisector creates identical 45˚ - 45˚ - 90˚ right triangles. This means that, if the sides of the square are 
then the diagonal must be 
. We can then set up the following equation:
If 
then the area must be:
To solve this problem, we must recognize that the diagonal bisector creates identical 45˚ - 45˚ - 90˚ right triangles. This means that, if the sides of the square are
If
Is Rectangle 
a square?
Statement 1: 
Statement 2: 
Is Rectangle
Statement 1:
Statement 2:
Tap to see back →
A rectangle, by definition, is a parallelogram. Statement 1 asserts that the diagonals of this parallelogram are perpendicular. Statement 2 asserts that adjacent sides of the parallelogram are congruent, so, since opposite sides are also congruent, this makes all four sides congruent. From either statement alone, it can be deduced that Rectangle 
is a rhombus. A figure that is a rectangle and a rhombus is by definition a square.
A rectangle, by definition, is a parallelogram. Statement 1 asserts that the diagonals of this parallelogram are perpendicular. Statement 2 asserts that adjacent sides of the parallelogram are congruent, so, since opposite sides are also congruent, this makes all four sides congruent. From either statement alone, it can be deduced that Rectangle
Find the side length of square R.
I) The area of square R is 
.
II) The perimeter of square R is 
.
Find the side length of square R.
I) The area of square R is
II) The perimeter of square R is
Tap to see back →
Consider the following equations:
Where a is area, p is perimeter, and s is side length
We can find the side length with either our area or our perimeter.
Thus, we only need one statment or the other.
Consider the following equations:
Where a is area, p is perimeter, and s is side length
We can find the side length with either our area or our perimeter.
Thus, we only need one statment or the other.
What is the length of the side of square 
, knowing that 
is the midpoint of diagonal 
?
(1) 
(2) 
What is the length of the side of square
(1)
(2)
Tap to see back →
Since ABCD is a square, we just need to know the length of the diagonale to find the length of the side. BE is half the diagonal, therefore knowing its length would help us find the length of the sides.
Statement 1 tells us the length of BE, therefore, with the formula 
where 
is the diagonal and 
the length of side, we can find the length of the side.
Statement 2 tells us that triangle AEB is isoceles, but it is something we could already have known from the beginning since we are told that E is the midpoint of the diagonal.
Therefore, statement 1 alone is sufficient.
Since ABCD is a square, we just need to know the length of the diagonale to find the length of the side. BE is half the diagonal, therefore knowing its length would help us find the length of the sides.
Statement 1 tells us the length of BE, therefore, with the formula
Statement 2 tells us that triangle AEB is isoceles, but it is something we could already have known from the beginning since we are told that E is the midpoint of the diagonal.
Therefore, statement 1 alone is sufficient.
Find the area of square 
.
I) 
has a diagonal of 
inches.
II) 
has a perimeter of 
inches.
Find the area of square
I)
II)
Tap to see back →
To find the area of a square we need to find its side length.
In a square, the diagonal allows us to find the other two sides. The diagonal of a square creates two 45/45/90 triangles with special side length ratios.
I) Gives us the diagonal, which we can use to find the side length, which will then help us find the area.
II) Perimeter of a square allows us to find side length, which in turn lets us find area.
So, either statement is sufficient.
To find the area of a square we need to find its side length.
In a square, the diagonal allows us to find the other two sides. The diagonal of a square creates two 45/45/90 triangles with special side length ratios.
I) Gives us the diagonal, which we can use to find the side length, which will then help us find the area.
II) Perimeter of a square allows us to find side length, which in turn lets us find area.
So, either statement is sufficient.