DSQ: Calculating the length of the diagonal of a square - GMAT Quantitative

Card 0 of 48

Question

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.

Answer

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.

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Question

The circle with center is inscribed in square . What is the length of diagonal ?

(1) The area of the circle is $16\pi$ .

(2) The side of the square is .

Answer

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.

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Question

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.

Answer

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)

$P=4s \rightarrow 60=4s \rightarrow 15=s$

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.

$c=\sqrt{450}=15\sqrt2$

From Statement II)

$225=s^2 \rightarrow 15=s$

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.

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Question

What is the length of the diagonal of the square?

The area of the square is $64 cm^{2}$ .

The perimeter is .

Answer

The length of the diagonal of a square is given by $s\sqrt{2}$ , where represents the square's side. As such, we need the length of the square's side.

Statement 1:

$s=\sqrt{64}=8 cm$

Statement 2:

$s=\frac{32}{4}=8cm$

Both statements provide us with the length of the square's side.

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Question

Find the length of the diagonal of square A if the diagonal of square B is $8\sqrt{2}in$ .

The perimeter of square B is

The area of square A is

Answer

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: $d=s\sqrt{2}=4\sqrt{2}in$

Compare your answer with the correct one above

Question

The diagonal bracing of a square pallet measures $6\textup{ m}$ . What is the area of the pallet?

Answer

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 $x\sqrt{2}$ . We can then set up the following equation:

$6 = x\sqrt{2} \Rightarrow x = 6/\sqrt{2} \Rightarrow x = 3\sqrt{2}$

If $x = 3\sqrt{2}$ then the area must be: $A = (3\sqrt2)^2 = 9 \cdot2 = 18$

Compare your answer with the correct one above

Question

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.

Answer

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.

Compare your answer with the correct one above

Question

The circle with center is inscribed in square . What is the length of diagonal ?

(1) The area of the circle is $16\pi$ .

(2) The side of the square is .

Answer

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.

Compare your answer with the correct one above

Question

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.

Answer

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)

$P=4s \rightarrow 60=4s \rightarrow 15=s$

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.

$c=\sqrt{450}=15\sqrt2$

From Statement II)

$225=s^2 \rightarrow 15=s$

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.

Compare your answer with the correct one above

Question

What is the length of the diagonal of the square?

The area of the square is $64 cm^{2}$ .

The perimeter is .

Answer

The length of the diagonal of a square is given by $s\sqrt{2}$ , where represents the square's side. As such, we need the length of the square's side.

Statement 1:

$s=\sqrt{64}=8 cm$

Statement 2:

$s=\frac{32}{4}=8cm$

Both statements provide us with the length of the square's side.

Compare your answer with the correct one above

Question

Find the length of the diagonal of square A if the diagonal of square B is $8\sqrt{2}in$ .

The perimeter of square B is

The area of square A is

Answer

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: $d=s\sqrt{2}=4\sqrt{2}in$

Compare your answer with the correct one above

Question

The diagonal bracing of a square pallet measures $6\textup{ m}$ . What is the area of the pallet?

Answer

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 $x\sqrt{2}$ . We can then set up the following equation:

$6 = x\sqrt{2} \Rightarrow x = 6/\sqrt{2} \Rightarrow x = 3\sqrt{2}$

If $x = 3\sqrt{2}$ then the area must be: $A = (3\sqrt2)^2 = 9 \cdot2 = 18$

Compare your answer with the correct one above

Question

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.

Answer

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.

Compare your answer with the correct one above

Question

The circle with center is inscribed in square . What is the length of diagonal ?

(1) The area of the circle is $16\pi$ .

(2) The side of the square is .

Answer

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.

Compare your answer with the correct one above

Question

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.

Answer

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)

$P=4s \rightarrow 60=4s \rightarrow 15=s$

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.

$c=\sqrt{450}=15\sqrt2$

From Statement II)

$225=s^2 \rightarrow 15=s$

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.

Compare your answer with the correct one above

Question

What is the length of the diagonal of the square?

The area of the square is $64 cm^{2}$ .

The perimeter is .

Answer

The length of the diagonal of a square is given by $s\sqrt{2}$ , where represents the square's side. As such, we need the length of the square's side.

Statement 1:

$s=\sqrt{64}=8 cm$

Statement 2:

$s=\frac{32}{4}=8cm$

Both statements provide us with the length of the square's side.

Compare your answer with the correct one above

Question

Find the length of the diagonal of square A if the diagonal of square B is $8\sqrt{2}in$ .

The perimeter of square B is

The area of square A is

Answer

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: $d=s\sqrt{2}=4\sqrt{2}in$

Compare your answer with the correct one above

Question

The diagonal bracing of a square pallet measures $6\textup{ m}$ . What is the area of the pallet?

Answer

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 $x\sqrt{2}$ . We can then set up the following equation:

$6 = x\sqrt{2} \Rightarrow x = 6/\sqrt{2} \Rightarrow x = 3\sqrt{2}$

If $x = 3\sqrt{2}$ then the area must be: $A = (3\sqrt2)^2 = 9 \cdot2 = 18$

Compare your answer with the correct one above

Question

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.

Answer

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.

Compare your answer with the correct one above

Question

The circle with center is inscribed in square . What is the length of diagonal ?

(1) The area of the circle is $16\pi$ .

(2) The side of the square is .

Answer

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.

Compare your answer with the correct one above

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