Quadrilaterals - GMAT Quantitative
Card 1 of 1104
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.
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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
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A square plot of land has area 256 square yards. Give its perimeter in inches.
A square plot of land has area 256 square yards. Give its perimeter in inches.
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The sidelength of a square is the square root of its area - in this case, 
yards. Its perimeter is therefore four times that, or 
yards. Multiply by 36 to convert to inches:
inches.
The sidelength of a square is the square root of its area - in this case,
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Five squares have sidelengths 3, 4, 5, 6, and 7 meters. What is the mean of their perimeters?
Five squares have sidelengths 3, 4, 5, 6, and 7 meters. What is the mean of their perimeters?
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Multiply each sidelength by four to get the perimeters - they will be 12, 16, 20, 24, and 28 meters, respectively. The mean will be
meters
Multiply each sidelength by four to get the perimeters - they will be 12, 16, 20, 24, and 28 meters, respectively. The mean will be
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Given Square 
, answer the following questions.
Square 
represents a small field for a farmer's sheep. How many meters of fence will the farmer require to completely enclose the field?
Given Square
Square
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This question is a thinly veiled perimeter of a square question. To find the total amount of fencing needed, use the following formula:
Where 
is the perimeter of a square, and 
is the length of one side.
This question is a thinly veiled perimeter of a square question. To find the total amount of fencing needed, use the following formula:
Where
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A given square has a side length of 
. What is its perimeter?
A given square has a side length of
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In order to find the perimeter 
of a given square with side length 
, we use the equation 
. Given 
, we can therefore conclude that 
.
In order to find the perimeter
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A given square has an area of 
. What is its perimeter?
A given square has an area of
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We are told that the area 
of the square is 
. We know the area of a square is defined as 
, where 
is the length of the side of the square. We can therefore deduce that 
and that 
.
In order to find the perimeter 
of a given square with side length 
, we use the equation 
. Given 
, we can therefore conclude that 
.
We are told that the area
In order to find the perimeter
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A given square has a side of length 
. What is the perimeter of the square?
A given square has a side of length
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In order to find the perimeter 
of a given square with side length 
, we use the equation 
. Given 
, we can therefore conclude that 
.
In order to find the perimeter
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The area of a square that has sides with a length of 12 inches is equal to the area of a rectangle. If the rectangle has a width of 3 inches, what is the length of the rectangle?
The area of a square that has sides with a length of 12 inches is equal to the area of a rectangle. If the rectangle has a width of 3 inches, what is the length of the rectangle?
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If the area of the rectangle is equal to the area of the square, then it must have an area of 
. If the rectangle has an area of 
and a side with a lenth of 3 inches, then the equation to solve the problem would be 
, where 
is the length of the rectangle. The solution:
.
If the area of the rectangle is equal to the area of the square, then it must have an area of
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Note: figure NOT drawn to scale
Give the area of the above rectangle.
Note: figure NOT drawn to scale
Give the area of the above rectangle.
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The area of a rectangle is the product of its length and width;
The area of a rectangle is the product of its length and width;
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A rectangle twice as long as it is wide has perimeter 
. Write its area in terms of 
.
A rectangle twice as long as it is wide has perimeter
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Let 
be the width of the rectangle; then its length is 
, and its perimeter is
Set this equal to 
and solve for 
:
The width is 
and the length is 
, so multiply these expressions to get the area:
Let
Set this equal to
The width is
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A rectangle has its vertices at 
. What part, in percent, of the rectangle is located in Quadrant III?
A rectangle has its vertices at
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A rectangle with vertices 
has width 
and height 
, thereby having area 
.
The portion of the rectangle in Quadrant III is a rectangle with vertices
.
It has width 
and height 
, thereby having area 
.
Therefore, 
of the rectangle is in Quadrant III; this is equal to
A rectangle with vertices
The portion of the rectangle in Quadrant III is a rectangle with vertices
It has width
Therefore,
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A rectangle has its vertices at 
. What percentage of the rectangle is located in Quadrant IV?
A rectangle has its vertices at
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A rectangle with vertices has width and height ; it follows that its area is .
The portion of the rectangle in Quadrant IV has vertices 
. Its width is 
, and its height is 
, so its area is 
.
Therefore, 
, or 
, of this rectangle is in Quadrant IV.
A rectangle with vertices
The portion of the rectangle in Quadrant IV has vertices
Therefore,
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What is the area of a rectangle given the length of 
and width of 
?
What is the area of a rectangle given the length of
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To find the area of a rectangle, you must use the following formula:
To find the area of a rectangle, you must use the following formula:
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Find the perimeter of a rectangle whose width is 
and length is 
.
Find the perimeter of a rectangle whose width is
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To solve, simply use the formula for the perimeter of a rectangle:
To solve, simply use the formula for the perimeter of a rectangle:
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What polynomial represents the area of a rectangle with length 
and width 
?
What polynomial represents the area of a rectangle with length
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The area of a rectangle is the product of the length and the width. The expression 
can be multplied by noting that this is the product of the sum and the difference of the same two terms; its product is the difference of the squares of the terms, or
The area of a rectangle is the product of the length and the width. The expression
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The perimeter of a rectangle is 
and its length is 
times the width. What is the area?
The perimeter of a rectangle is
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The perimeter of a rectangle is the sum of all four sides, that is: 
since 
, we can rewrite the equation as:
We are being asked for the area so we still aren't done. The area of a rectangle is the product of the width and length. We know what the width is so we can find the length and then take their product.
The perimeter of a rectangle is the sum of all four sides, that is:
since
We are being asked for the area so we still aren't done. The area of a rectangle is the product of the width and length. We know what the width is so we can find the length and then take their product.
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Find the area of a rectangle whose side lengths are 
.
Find the area of a rectangle whose side lengths are
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To calculate area, multiply width times height. Thus,
To calculate area, multiply width times height. Thus,
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Mark is building a garden with raised beds. One side of the garden will be 10 feet long and the other will be 5 less than three times the first side. What area of will Mark's garden be?
Mark is building a garden with raised beds. One side of the garden will be 10 feet long and the other will be 5 less than three times the first side. What area of will Mark's garden be?
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Mark is building a garden with raised beds. One side of the garden will be 10 feet long and the other will be 5 less than three times the first side. What area of will Mark's garden be?
This problem asks us to find the area of a rectangle. We are given one side and asked to find the other. To find the other, we need to use the provided clues.
"...five less..." 
"...three times the first side..." 
or 
So put it together:
Next, find the area via the following formula:
So our answer is:
Mark is building a garden with raised beds. One side of the garden will be 10 feet long and the other will be 5 less than three times the first side. What area of will Mark's garden be?
This problem asks us to find the area of a rectangle. We are given one side and asked to find the other. To find the other, we need to use the provided clues.
"...five less..."
"...three times the first side..."
So put it together:
Next, find the area via the following formula:
So our answer is:
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Find the area of a rectangle whose width is 
and length is 
.
Find the area of a rectangle whose width is
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To find area, simply multiply length times width. Thus
To find area, simply multiply length times width. Thus
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A rectangle has a length of 
and a width of 
. What is the length of the diagonal of the rectangle?
A rectangle has a length of
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If the rectangle has a length of 
and a width of 
, we can imagine the diagonal as being the hypotenuse of a right triangle. The length and width are the other two sides to this triangle, so we can use the Pythagorean Theorem to calculate the length of the diagonal of the rectangle:
If the rectangle has a length of
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