GMAT Math : Calculating the perimeter of a square

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Example Question #1 : Calculating The Perimeter Of A Square

A square plot of land has area 256 square yards. Give its perimeter in inches.

Possible Answers:

$2,592\textrm{ in}$

$1,152 \textrm{ in}$

$4,608 \textrm{ in}$

$2,304 \textrm{ in}$

$1,296 \textrm{ in}$

Correct answer:

$2,304 \textrm{ in}$

Explanation:

The sidelength of a square is the square root of its area - in this case, $\sqrt{256} = 16$ yards. Its perimeter is therefore four times that, or $16 \times 4 = 64$ yards. Multiply by 36 to convert to inches:

$64 \times36 = 2,304$ inches.

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Example Question #2 : Calculating The Perimeter Of A Square

Five squares have sidelengths 3, 4, 5, 6, and 7 meters. What is the mean of their perimeters?

Possible Answers:

$16 \textrm{ m}$

$10 \textrm{ m}$

$27 \textrm{ m}$

$25 \textrm{ m}$

$20 \textrm{ m}$

Correct answer:

$20 \textrm{ m}$

Explanation:

Multiply each sidelength by four to get the perimeters - they will be 12, 16, 20, 24, and 28 meters, respectively. The mean will be

$\left (12+ 16 + 20 + 24 + 28 \right ) \div 5 = 100 \div 5 = 20$ meters

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Example Question #2 : Calculating The Perimeter Of A Square

Given Square FGHI , answer the following questions.

Square1

Square FGHI represents a small field for a farmer's sheep. How many meters of fence will the farmer require to completely enclose the field?

Possible Answers:

$225\:m$

$60\:m$

$45\:m$

$30\:m$

$120\:m$

Correct answer:

$60\:m$

Explanation:

This question is a thinly veiled perimeter of a square question. To find the total amount of fencing needed, use the following formula:

P=4*s

Where is the perimeter of a square, and is the length of one side.

$P=4*15\:meters=60 \:meters$

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Example Question #3 : Calculating The Perimeter Of A Square

A given square has a side length of 7cm . What is its perimeter?

Possible Answers:

Not enough information provided

28cm

49cm

$28cm^{2}$

$49cm^{2}$

Correct answer:

28cm

Explanation:

In order to find the perimeter of a given square with side length , we use the equation P=4s . Given s=7cm , we can therefore conclude that P=4(7cm)=28cm .

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Example Question #2 : Calculating The Perimeter Of A Square

A given square has an area of . What is its perimeter?

Possible Answers:

128

Not enough information provided

Correct answer:

Explanation:

We are told that the area of the square is . We know the area of a square is defined as $A=s^{2}$ , where is the length of the side of the square. We can therefore deduce that $64=s^{2}$ and that s=8 .

In order to find the perimeter of a given square with side length , we use the equation P=4s . Given s=8 , we can therefore conclude that P=4(8)=32 .

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Example Question #4 : Calculating The Perimeter Of A Square

A given square has a side of length 19cm . What is the perimeter of the square?

Possible Answers:

$76cm^{2}$

361cm

Not enough information provided

$361cm^{2}$

76cm

Correct answer:

76cm

Explanation:

In order to find the perimeter of a given square with side length , we use the equation P=4s . Given s=19cm , we can therefore conclude that P=4(19cm)=76cm .

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Example Question #7 : Calculating The Perimeter Of A Square

The area of a square is $4 ^{d}$ . Give its perimeter.

Possible Answers:

$4 ^{\frac{1}{2}d + \frac{1}{2}}$

$4 ^{ d - 1}$

$4 ^{ d + 1}$

$4 ^{ d -\frac{1}{2}}$

$4 ^{\frac{1}{2}d + 1}$

Correct answer:

$4 ^{\frac{1}{2}d + 1}$

Explanation:

The length of one side of a square is the square root of the area - or, equivalently, the area raised to the power of $\frac{1}{2}$ . Here, this is

$\left (4 ^{d} \right )^{\frac{1}{2}} = 4 ^{d \cdot \frac{1}{2}} = 4 ^{\frac{1}{2}d }$ .

Multiply this by 4 to get the perimeter:

$4 ^{\frac{1}{2}d } \cdot 4 = 4 ^{\frac{1}{2}d } \cdot 4 ^{1} = 4 ^{\frac{1}{2}d + 1}$

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Example Question #8 : Calculating The Perimeter Of A Square

A square courtyard will have paths running diagonally across it (the paths will form an x). If the length of one of the paths will be $14\sqrt{2}meters$ long, what will the perimeter of the courtyard be?

Possible Answers:

64meters

36meters

14meters

56meters

Correct answer:

56meters

Explanation:

To find the perimeter of a square, we need to find the side lengths. We can find the side lengths from the diagonal by recalling that the diagonal of a square creates two 45/45/90 triangles.

A 45/45/90 triangle has the following side-length ratios: $1/1/\sqrt{2}$

This means that if our hypotenuse is $14\sqrt{2}meters$ long, our other two sides will be 14 meters long

So our side-length is 14 meters, find the perimeter via the following

P=4s=14*4=56meters

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Example Question #71 : Quadrilaterals

A square is created from joining two equilateral triangles of side length = $4\textup{m}.$ What is the perimeter of the square?

Possible Answers:

$16\textup{m}^2$

$\textup{20m}$

$\textup{16m}$

$20\textup{m}^2$

$\textup{8m}$

Correct answer:

$\textup{16m}$

Explanation:

Draw yourself a picture for this problem. If you create a square out of two triangles, they meet at the diagonal of the square. Since, we know the triangles are equilateral, then all of the side lengths of the triangle and square are equal. Therefore, we just take the side length and add that four times.

$\textup{4m +4m +4m+4m=16m.}$

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GMAT Math : Calculating the perimeter of a square

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Perimeter Of A Square

Example Question #2 : Calculating The Perimeter Of A Square

Example Question #2 : Calculating The Perimeter Of A Square

Example Question #3 : Calculating The Perimeter Of A Square

Example Question #2 : Calculating The Perimeter Of A Square

Example Question #4 : Calculating The Perimeter Of A Square

Example Question #7 : Calculating The Perimeter Of A Square

Example Question #8 : Calculating The Perimeter Of A Square

Example Question #71 : Quadrilaterals

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