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Pre-Algebra : Perimeter of a Rectangle or Square

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Example Questions

Example Question #11 : Perimeter Of A Rectangle Or Square

If the diagonal of a square is $6\sqrt2$ $\displaystyle 6\sqrt2$, what is the perimeter?

Possible Answers:

$48\sqrt2$ $\displaystyle 48\sqrt2$

$\displaystyle 12$

$\displaystyle 18$

$24\sqrt2$ $\displaystyle 24\sqrt2$

$\displaystyle 24$

Correct answer:

$\displaystyle 24$

Explanation:

Write the formula to obtain the side given the diagonal for squares.

$s=\frac{d}{\sqrt2} = \frac{6\sqrt2}{\sqrt2} =6$ $\displaystyle s=\frac{d}{\sqrt2} = \frac{6\sqrt2}{\sqrt2} =6$

The perimeter of the square is four times the side.

The answer is $\displaystyle 24$.

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Example Question #12 : Perimeter Of A Rectangle Or Square

What is the perimeter of a square with a side length of x-2y $\displaystyle x-2y$?

Possible Answers:

-4xy $\displaystyle -4xy$

8xy $\displaystyle 8xy$

4x-y $\displaystyle 4x-y$

4x-8y $\displaystyle 4x-8y$

8x-y $\displaystyle 8x-y$

Correct answer:

4x-8y $\displaystyle 4x-8y$

Explanation:

Write the formula to find the perimeter of a square.

P=4s $\displaystyle P=4s$

Substitute the side.

$\displaystyle P=4(x-2y) = 4x-8y$

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Example Question #13 : Perimeter Of A Rectangle Or Square

Find the perimeter of a square in feet if the side length is 8 inches.

Possible Answers:

$\displaystyle 32$

384 $\displaystyle 384$

$\displaystyle 64$

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

$\displaystyle 2$

Correct answer:

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

Explanation:

Convert the 8 inches to feet by dividing 12. There are 12 inches in a foot.

$8\textup{ inches }= \frac{8}{12} \textup{ foot} = \frac{2}{3}\textup{ foot}$ $\displaystyle 8\textup{ inches }= \frac{8}{12} \textup{ foot} = \frac{2}{3}\textup{ foot}$

Write the formula for the perimeter of a square.

P=4s $\displaystyle P=4s$

Substitute the side.

$P=4 (\frac{2}{3}) = \frac{8}{3}$ $\displaystyle P=4 (\frac{2}{3}) = \frac{8}{3}$

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Example Question #13 : Perimeter Of A Rectangle Or Square

Determine the perimeter of a square with an area of 5.

Possible Answers:

$\displaystyle 20$

$2\sqrt{10}$ $\displaystyle 2\sqrt{10}$

$\displaystyle 4$

$2\sqrt{5}$ $\displaystyle 2\sqrt{5}$

$4\sqrt5$ $\displaystyle 4\sqrt5$

Correct answer:

$4\sqrt5$ $\displaystyle 4\sqrt5$

Explanation:

Write the formula for the area of a square.

A=s^2 $\displaystyle A=s^2$

Substitute the area and find the side.

5=s^2 $\displaystyle 5=s^2$

$s=\sqrt5$ $\displaystyle s=\sqrt5$

A square has four equal sides. Multiply this side by four.

$P=4s= 4\sqrt5$ $\displaystyle P=4s= 4\sqrt5$

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Example Question #13 : Perimeter Of A Rectangle Or Square

Find the perimeter of a square with a side of $2\pi +1$ $\displaystyle 2\pi +1$.

Possible Answers:

$4\pi^2 +2$ $\displaystyle 4\pi^2 +2$

$8\pi +4$ $\displaystyle 8\pi +4$

$8\pi +2$ $\displaystyle 8\pi +2$

$4\pi^2 +1$ $\displaystyle 4\pi^2 +1$

$12\pi$ $\displaystyle 12\pi$

Correct answer:

$8\pi +4$ $\displaystyle 8\pi +4$

Explanation:

Write the perimeter formula for a square.

P=4s $\displaystyle P=4s$

Substitute the side. Remember to distribute the four to each term within the parentheses.

$P=4(2\pi +1) = 8\pi +4$ $\displaystyle P=4(2\pi +1) = 8\pi +4$

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Example Question #15 : Perimeter Of A Rectangle Or Square

Find the perimeter of a square with a side of 9x^2 $\displaystyle 9x^2$.

Possible Answers:

81x^4 $\displaystyle 81x^4$

36x^6 $\displaystyle 36x^6$

81x^2 $\displaystyle 81x^2$

36x^4 $\displaystyle 36x^4$

36x^2 $\displaystyle 36x^2$

Correct answer:

36x^2 $\displaystyle 36x^2$

Explanation:

Since the square has four equal sides, the perimeter is four times the side of the square. Write the formula to find the perimeter of a square. The variable $\displaystyle s$ represents the side length.

P=4s $\displaystyle P=4s$

Substitute the side length into the formula.

$P=4(9x^2) = 4\cdot 9 \cdot x\cdot x =36x^2$ $\displaystyle P=4(9x^2) = 4\cdot 9 \cdot x\cdot x =36x^2$

The area of the square is 36x^2 $\displaystyle 36x^2$.

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Example Question #296 : Geometry

If all sides of this square are equal, find its perimeter.

Perimeter

Possible Answers:

$49\ in$ $\displaystyle 49\ in$

$28\ in$ $\displaystyle 28\ in$

$7\ in$ $\displaystyle 7\ in$

$14\ in$ $\displaystyle 14\ in$

$21\ in$ $\displaystyle 21\ in$

Correct answer:

$28\ in$ $\displaystyle 28\ in$

Explanation:

The perimeter of a shape is the total length of all sides.

Perimeter

With this shape, we know that all of its sides are equal. So, we know that each side is 7 in.

Perimeter 2

Using the definition of perimeter, we will find the total length of all the sides. To do this, we simply add all the lengths together.

7 in + 7 in + 7 in + 7 in = 28 in

So, the perimeter of this square is 28 in.

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Example Question #18 : Perimeter Of A Rectangle Or Square

A squares sides measure $\displaystyle 3$ inches each. What is its perimeter?

Possible Answers:

$\displaystyle 9$ $\displaystyle in$

$\displaystyle 12$ $\displaystyle in$

$\displaystyle 14$ $\displaystyle in$

$\displaystyle 11$ $\displaystyle in$

$\displaystyle 15$ $\displaystyle in$

Correct answer:

$\displaystyle 12$ $\displaystyle in$

Explanation:

To find the perimeter of any object, simply add the length of each side together.

The best answer is:

$P=4s=4\times 3=12$ $\displaystyle P=4s=4\times 3=12$

$\displaystyle 12$ $\displaystyle in$

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Example Question #19 : Perimeter Of A Rectangle Or Square

A squares sides measure $\displaystyle 2$ inches each. What is its perimeter?

Possible Answers:

$\displaystyle 11$ $\displaystyle in$

$\displaystyle 12$ $\displaystyle in$

$\displaystyle 10$ $\displaystyle in$

$\displaystyle 8$ $\displaystyle in$

$\displaystyle 9$ $\displaystyle in$

Correct answer:

$\displaystyle 8$ $\displaystyle in$

Explanation:

To find the perimeter of any object, simply add the length of each side together.

The best answer is:

$P=s+s+s+s=4s=4\times 2=8$ $\displaystyle P=s+s+s+s=4s=4\times 2=8$

$\displaystyle 8$ $\displaystyle in$

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Example Question #14 : Perimeter Of A Rectangle Or Square

A rectangle measures ten inches along its short side, and twelve inches along its long side. What is the perimeter of the rectangle?

Possible Answers:

thirty four inches

twenty four inches

fourty six inches

fourty four inches

fourty five inches

Correct answer:

fourty four inches

Explanation:

To find the perimeter of any object, simply add the length of each side together.

The best answer is:

$\\P=2s_1+2s_2\\=2(10)+2(12)\\=20+24\\=44$ $\displaystyle \\P=2s_1+2s_2\\=2(10)+2(12)\\=20+24\\=44$

fourty four inches

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Pre-Algebra : Perimeter of a Rectangle or Square

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Perimeter Of A Rectangle Or Square

Example Question #12 : Perimeter Of A Rectangle Or Square

Example Question #13 : Perimeter Of A Rectangle Or Square

Example Question #13 : Perimeter Of A Rectangle Or Square

Example Question #13 : Perimeter Of A Rectangle Or Square

Example Question #15 : Perimeter Of A Rectangle Or Square

Example Question #296 : Geometry

Example Question #18 : Perimeter Of A Rectangle Or Square

Example Question #19 : Perimeter Of A Rectangle Or Square

Example Question #14 : Perimeter Of A Rectangle Or Square

All Pre-Algebra Resources

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