Calculating the length of the side of a square - GMAT Quantitative
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Square A has twice the sidelength of Square B. The total area of the squares is 605 square feet. What is the sidelength of Square B?
Square A has twice the sidelength of Square B. The total area of the squares is 605 square feet. What is the sidelength of Square B?
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Let 
be the sidelength of Square B. Then the sidelength of Square A is 
, and the areas of Squares A and B are 
and 
, respectively. Since the areas add up to 605 square feet, we solve for 
in this equation:
feet
Let
A circle is inscribed in a square. The area of the circle is 
. What is the area of the square?
A circle is inscribed in a square. The area of the circle is
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Since we know the area of the circle, we can tell that: 
. Where 
is the radius of the circle.
The length of a side of the square will be 
since the diameter of the circle is the same length as the side length of the square.
Finally we can calculate the area of the square which will be 
. 
so the area will be 
, which is our final answer.
Since we know the area of the circle, we can tell that:
The length of a side of the square will be
Finally we can calculate the area of the square which will be
A circle is inscribed in a square. The square has an area of 
, what is the perimeter of the circle?
A circle is inscribed in a square. The square has an area of
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The square as an area of 3. From that we can figure out the length of a side of the square, which is the same size as the diameter of the circle.
From the diameter of the circle we can find out, the perimeter of the circle given by the formula: 
, where 
is the length of the diamter.
So 
and therefore, the final answer is 
.
The square as an area of 3. From that we can figure out the length of a side of the square, which is the same size as the diameter of the circle.
From the diameter of the circle we can find out, the perimeter of the circle given by the formula:
So
is a square, and 
is the midpoint of diagonal 
. 
. What is the length of the side of the square?
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Since BE is half of the diagonal BD, it follows that the size of the diagonal must be 
.
The length of a diagonal of a square will always be 
, where 
is the length of the side of the square.
Since the diagonal is 
, the side of the square must be 2.
Since BE is half of the diagonal BD, it follows that the size of the diagonal must be
The length of a diagonal of a square will always be
Since the diagonal is
The perimeter of a square plus its area is equal to 
. What is the length of a side of the square?
The perimeter of a square plus its area is equal to
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First we must set up the equation described by the first sentence of the problem. It tells us the perimeter of a square plus its area is equal to 
. We want to write this in terms of length, so we can write the following:
Where 
is the length of one side of the square. We then bring over the 
to write the equation as a polynomial that we can factor. This gives us:
A negative length makes no sense, so we can cross out the first result and we're left with the answer, 
. We could plug this length back into the original formula and see that a square with this side length would have a perimeter of 
and an area of 
, which add up to 
, verifying the solution.
First we must set up the equation described by the first sentence of the problem. It tells us the perimeter of a square plus its area is equal to
Where
A negative length makes no sense, so we can cross out the first result and we're left with the answer,
Two squares in the same plane have the same center. The length of one side of the larger square is 10; the area of the region between the squares is 60. Give the length of one side of the smaller square.
Two squares in the same plane have the same center. The length of one side of the larger square is 10; the area of the region between the squares is 60. Give the length of one side of the smaller square.
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Let 
be the length of one side of the smaller square. Then the smaller square has area 
; the larger square has area 
. The area of the region between them, 60, is their difference:
Let
Two squares in the same plane have the same center. The length of one side of the smaller square is 10; the area of the region between the squares is 60. Give the length of one side of the larger square.
Two squares in the same plane have the same center. The length of one side of the smaller square is 10; the area of the region between the squares is 60. Give the length of one side of the larger square.
Tap to see back →
Let 
be the length of one side of the larger square. Then the larger square has area 
; the smaller square has area 
. The area of the region between them, 60, is their difference:
Let
Square A has twice the sidelength of Square B. The total area of the squares is 605 square feet. What is the sidelength of Square B?
Square A has twice the sidelength of Square B. The total area of the squares is 605 square feet. What is the sidelength of Square B?
Tap to see back →
Let be the sidelength of Square B. Then the sidelength of Square A is , and the areas of Squares A and B are and , respectively. Since the areas add up to 605 square feet, we solve for in this equation:
feet
Let
A circle is inscribed in a square. The area of the circle is . What is the area of the square?
A circle is inscribed in a square. The area of the circle is
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Since we know the area of the circle, we can tell that: . Where is the radius of the circle.
The length of a side of the square will be since the diameter of the circle is the same length as the side length of the square.
Finally we can calculate the area of the square which will be . so the area will be , which is our final answer.
Since we know the area of the circle, we can tell that:
The length of a side of the square will be
Finally we can calculate the area of the square which will be
A circle is inscribed in a square. The square has an area of , what is the perimeter of the circle?
A circle is inscribed in a square. The square has an area of
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The square as an area of 3. From that we can figure out the length of a side of the square, which is the same size as the diameter of the circle.
From the diameter of the circle we can find out, the perimeter of the circle given by the formula: , where is the length of the diamter.
So and therefore, the final answer is .
The square as an area of 3. From that we can figure out the length of a side of the square, which is the same size as the diameter of the circle.
From the diameter of the circle we can find out, the perimeter of the circle given by the formula:
So
is a square, and is the midpoint of diagonal . . What is the length of the side of the square?
Tap to see back →
Since BE is half of the diagonal BD, it follows that the size of the diagonal must be .
The length of a diagonal of a square will always be , where is the length of the side of the square.
Since the diagonal is , the side of the square must be 2.
Since BE is half of the diagonal BD, it follows that the size of the diagonal must be
The length of a diagonal of a square will always be
Since the diagonal is
The perimeter of a square plus its area is equal to . What is the length of a side of the square?
The perimeter of a square plus its area is equal to
Tap to see back →
First we must set up the equation described by the first sentence of the problem. It tells us the perimeter of a square plus its area is equal to . We want to write this in terms of length, so we can write the following:
Where is the length of one side of the square. We then bring over the to write the equation as a polynomial that we can factor. This gives us:
A negative length makes no sense, so we can cross out the first result and we're left with the answer, . We could plug this length back into the original formula and see that a square with this side length would have a perimeter of and an area of , which add up to , verifying the solution.
First we must set up the equation described by the first sentence of the problem. It tells us the perimeter of a square plus its area is equal to
Where
A negative length makes no sense, so we can cross out the first result and we're left with the answer,
Two squares in the same plane have the same center. The length of one side of the larger square is 10; the area of the region between the squares is 60. Give the length of one side of the smaller square.
Two squares in the same plane have the same center. The length of one side of the larger square is 10; the area of the region between the squares is 60. Give the length of one side of the smaller square.
Tap to see back →
Let be the length of one side of the smaller square. Then the smaller square has area ; the larger square has area . The area of the region between them, 60, is their difference:
Let
Two squares in the same plane have the same center. The length of one side of the smaller square is 10; the area of the region between the squares is 60. Give the length of one side of the larger square.
Two squares in the same plane have the same center. The length of one side of the smaller square is 10; the area of the region between the squares is 60. Give the length of one side of the larger square.
Tap to see back →
Let be the length of one side of the larger square. Then the larger square has area ; the smaller square has area . The area of the region between them, 60, is their difference:
Let
Square A has twice the sidelength of Square B. The total area of the squares is 605 square feet. What is the sidelength of Square B?
Square A has twice the sidelength of Square B. The total area of the squares is 605 square feet. What is the sidelength of Square B?
Tap to see back →
Let be the sidelength of Square B. Then the sidelength of Square A is , and the areas of Squares A and B are and , respectively. Since the areas add up to 605 square feet, we solve for in this equation:
feet
Let
A circle is inscribed in a square. The area of the circle is . What is the area of the square?
A circle is inscribed in a square. The area of the circle is
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Since we know the area of the circle, we can tell that: . Where is the radius of the circle.
The length of a side of the square will be since the diameter of the circle is the same length as the side length of the square.
Finally we can calculate the area of the square which will be . so the area will be , which is our final answer.
Since we know the area of the circle, we can tell that:
The length of a side of the square will be
Finally we can calculate the area of the square which will be
A circle is inscribed in a square. The square has an area of , what is the perimeter of the circle?
A circle is inscribed in a square. The square has an area of
Tap to see back →
The square as an area of 3. From that we can figure out the length of a side of the square, which is the same size as the diameter of the circle.
From the diameter of the circle we can find out, the perimeter of the circle given by the formula: , where is the length of the diamter.
So and therefore, the final answer is .
The square as an area of 3. From that we can figure out the length of a side of the square, which is the same size as the diameter of the circle.
From the diameter of the circle we can find out, the perimeter of the circle given by the formula:
So
is a square, and is the midpoint of diagonal . . What is the length of the side of the square?
Tap to see back →
Since BE is half of the diagonal BD, it follows that the size of the diagonal must be .
The length of a diagonal of a square will always be , where is the length of the side of the square.
Since the diagonal is , the side of the square must be 2.
Since BE is half of the diagonal BD, it follows that the size of the diagonal must be
The length of a diagonal of a square will always be
Since the diagonal is
The perimeter of a square plus its area is equal to . What is the length of a side of the square?
The perimeter of a square plus its area is equal to
Tap to see back →
First we must set up the equation described by the first sentence of the problem. It tells us the perimeter of a square plus its area is equal to . We want to write this in terms of length, so we can write the following:
Where is the length of one side of the square. We then bring over the to write the equation as a polynomial that we can factor. This gives us:
A negative length makes no sense, so we can cross out the first result and we're left with the answer, . We could plug this length back into the original formula and see that a square with this side length would have a perimeter of and an area of , which add up to , verifying the solution.
First we must set up the equation described by the first sentence of the problem. It tells us the perimeter of a square plus its area is equal to
Where
A negative length makes no sense, so we can cross out the first result and we're left with the answer,
Two squares in the same plane have the same center. The length of one side of the larger square is 10; the area of the region between the squares is 60. Give the length of one side of the smaller square.
Two squares in the same plane have the same center. The length of one side of the larger square is 10; the area of the region between the squares is 60. Give the length of one side of the smaller square.
Tap to see back →
Let be the length of one side of the smaller square. Then the smaller square has area ; the larger square has area . The area of the region between them, 60, is their difference:
Let