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Example Questions

Example Question #12 : Squares

A square garden has an area of 64 square feet. If you add 3 feet to each side, what is the new perimeter of the garden?

Possible Answers:

121

Correct answer:

Explanation:

By finding the square root of the area of the garden, you find the length of one side, which is 8. We add 3 feet to this, giving us 11, then multiply this by 4 to get 44 feet for the perimeter.

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Example Question #1 : How To Find The Perimeter Of A Square

The area of the shaded region of a square is 18. What is the perimeter of the square?

Possible Answers:

Correct answer:

Explanation:

The area of the shaded region, which covers half of the square is 18 meaning that the total area of the square is 18 x 2, or 36. The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6. The perimeter is the length of 1 side times 4 or 6 x 4.

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Example Question #162 : Quadrilaterals

The area of a square is $25 cm^{2}$ $\displaystyle 25 cm^{2}$. If the square is enlarged by a factor of 2, what is the perimeter of the new square?

Possible Answers:

$75\ cm$ $\displaystyle 75\ cm$

$40\ cm$ $\displaystyle 40\ cm$

$100\ cm$ $\displaystyle 100\ cm$

$50\ cm$ $\displaystyle 50\ cm$

$80\ cm$ $\displaystyle 80\ cm$

Correct answer:

$40\ cm$ $\displaystyle 40\ cm$

Explanation:

The area of a square is given by $A = s^{2}$ $\displaystyle A = s^{2}$ so we know the side is 5 cm. Enlarging by a factor of two makes the new side 10 cm. The perimeter is given by P = 4s $\displaystyle P = 4s$, so the perimeter of the new square is 40 cm.

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Example Question #4 : How To Find The Perimeter Of A Square

The diagonal of a square has a length of 10 inches. What is the perimeter of the square in inches squared?

Possible Answers:

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

$6\sqrt{2}$ $\displaystyle 6\sqrt{2}$

$20\sqrt{2}$ $\displaystyle 20\sqrt{2}$

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

Correct answer:

$20\sqrt{2}$ $\displaystyle 20\sqrt{2}$

Explanation:

Using the Pythagorean Theorem, we can find the edge of a side to be √50, by 2a²=10². This can be reduced to 5√2. This can then be multiplied by 4 to find the perimeter.

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Example Question #3 : How To Find The Perimeter Of A Square

What is the perimeter of a square with an area of $\displaystyle 36$?

Possible Answers:

$\displaystyle 24$

$\displaystyle 30$

$\displaystyle 36$

$\displaystyle 12$

$\displaystyle 16$

Correct answer:

$\displaystyle 24$

Explanation:

1. Find the side lengths:

$Area= (side)^{2}$ $\displaystyle Area= (side)^{2}$

$36=(side)^{2}$ $\displaystyle 36=(side)^{2}$

side=6 $\displaystyle side=6$

2. Use the side lengths to find the perimeter:

$\displaystyle Perimeter= 4(side)$

$\displaystyle Perimeter=4(6)=24$

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Example Question #1 : How To Find The Perimeter Of A Square

Find the perimeter of a square whose area is $\displaystyle 16$.

Possible Answers:

$\displaystyle 32$

$\displaystyle 64$

$\displaystyle 16$

$\displaystyle 4$

$\displaystyle 8$

Correct answer:

$\displaystyle 16$

Explanation:

To solve, you must first find the side length.

$s=\sqrt{A}=\sqrt{16}=4$ $\displaystyle s=\sqrt{A}=\sqrt{16}=4$

Then, you must multiply the side length by 4 since there are 4 sides. Thus,

$\displaystyle P=4*4=16$

In this case, volume and perimeter were the same numerical value, but this won't always be the case.

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Example Question #21 : Squares

Find the perimeter of a square with side length $\displaystyle 1$.

Possible Answers:

$\displaystyle 16$

$\displaystyle 1$

$\displaystyle 4$

$\displaystyle 2$

Correct answer:

$\displaystyle 4$

Explanation:

To find perimeter, simply multiply side length by $\displaystyle 4$. Thus,

$P=1\cdot 4=4$ $\displaystyle P=1\cdot 4=4$

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Example Question #171 : Quadrilaterals

The area of a square is $64\textup{ in}^2$ $\displaystyle 64\textup{ in}^2$, what is the perimeter of the square?

Possible Answers:

$\textup{36in}$ $\displaystyle \textup{36in}$

$\textup{32in}$ $\displaystyle \textup{32in}$

$\textup{Not enough information is provided.}$ $\displaystyle \textup{Not enough information is provided.}$

$\textup{16in}$ $\displaystyle \textup{16in}$

24in $\displaystyle 24in$

Correct answer:

$\textup{32in}$ $\displaystyle \textup{32in}$

Explanation:

Since the sides of a square are all the same, the area of a square can be found by $\textup{side}*\textup{side}=64\textup{in}^2.$ $\displaystyle \textup{side}*\textup{side}=64\textup{in}^2.$ Therefore, the side of the square must be $8\textup{in}.$ $\displaystyle 8\textup{in}.$ The perimeter of a square can be found by adding up all of the four sides: $\textup{8in+8in+8in+8in=32in.}$ $\displaystyle \textup{8in+8in+8in+8in=32in.}$

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Example Question #1 : How To Find The Length Of The Side Of A Square

If the area of the square is 100 square units, what is, in units, the length of one side of the square?

Possible Answers:

$\displaystyle 10$

$\displaystyle 5$

$\displaystyle 20$

$\displaystyle 25$

$\displaystyle 50$

Correct answer:

$\displaystyle 10$

Explanation:

$Area = Length \times Length$ $\displaystyle Area = Length \times Length$

$\displaystyle 100 = (Length)^2$

$Length = \sqrt{100}=10$ $\displaystyle Length = \sqrt{100}=10$

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Example Question #2 : How To Find The Length Of The Side Of A Square

In Square SQUA $\displaystyle SQUA$, $SU = \sqrt{2x}$ $\displaystyle SU = \sqrt{2x}$. Evaluate $\displaystyle SQ$ in terms of $\displaystyle x$.

Possible Answers:

$\displaystyle x$

$\sqrt{x}$ $\displaystyle \sqrt{x}$

$\displaystyle 2x$

$2\sqrt{x}$ $\displaystyle 2\sqrt{x}$

$x\sqrt{2}$ $\displaystyle x\sqrt{2}$

Correct answer:

$\sqrt{x}$ $\displaystyle \sqrt{x}$

Explanation:

If diagonal $\overline{SU}$ $\displaystyle \overline{SU}$ of Square SQUA $\displaystyle SQUA$ is constructed, then $\bigtriangleup SQU$ $\displaystyle \bigtriangleup SQU$ is a 45-45-90 triangle with hypotenuse $SU = \sqrt{2x}$ $\displaystyle SU = \sqrt{2x}$. By the 45-45-90 Theorem, the sidelength $\displaystyle SQ$ can be calculated as follows:

$SQ = \frac{SU}{\sqrt{2}} = \frac{\sqrt{2x}}{\sqrt{2}} = \sqrt{\frac{2x}{2}} = \sqrt{x}$ $\displaystyle SQ = \frac{SU}{\sqrt{2}} = \frac{\sqrt{2x}}{\sqrt{2}} = \sqrt{\frac{2x}{2}} = \sqrt{x}$.

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #12 : Squares

Example Question #1 : How To Find The Perimeter Of A Square

Example Question #162 : Quadrilaterals

Example Question #4 : How To Find The Perimeter Of A Square

Example Question #3 : How To Find The Perimeter Of A Square

Example Question #1 : How To Find The Perimeter Of A Square

Example Question #21 : Squares

Example Question #171 : Quadrilaterals

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #2 : How To Find The Length Of The Side Of A Square

All ACT Math Resources

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