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ACT Math : How to find the length of the diagonal of a square

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Example Questions

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

The perimeter of a square is 48. What is the length of its diagonal?

Possible Answers:

$\sqrt{12}$

$24\sqrt{2}$

$48\sqrt{2}$

$2\sqrt{12}$

$12\sqrt{2}$

Correct answer:

$12\sqrt{2}$

Explanation:

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

side^2 + side^2 = hypotenuse^2

12^2+12^2=hypotenuse^2

144 + 144=hypotenuse^2

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

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Example Question #143 : Quadrilaterals

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Possible Answers:

12.84

13.52

12.73

162

324

Correct answer:

162

Explanation:

Based on the data provided, the square could be drawn like this:

Squared18

Based on this, you can use the Pythagorean theorem to find :

x^2+x^2=18^2 or 2x^2=324

From this, you know that x^2=162

Since the area is equal to x^2 , this is your answer!

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Example Question #6 : How To Find The Length Of The Diagonal Of A Square

The perimeter of a square is units. How many units long is the diagonal of the square?

Possible Answers:

$14\sqrt2$

$7\sqrt2$

$14\sqrt3$

Correct answer:

$7\sqrt2$

Explanation:

From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,

4s=28

s=7

Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.

a^2+b^2=c^2

7^2+7^2=c^2

$c=\sqrt{49+49}=\sqrt{98}=\sqrt{2\cdot49}=7\sqrt2$

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

Find the diagonal of a square with side length .

Possible Answers:

$3\sqrt2$

Correct answer:

$3\sqrt2$

Explanation:

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

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Example Question #381 : Geometry

Find the length of a diagonal of a square whose side length is .

Possible Answers:

$\sqrt{2}$

Correct answer:

$\sqrt{2}$

Explanation:

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

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ACT Math : How to find the length of the diagonal of a square

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #143 : Quadrilaterals

Example Question #6 : How To Find The Length Of The Diagonal Of A Square

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

Example Question #381 : Geometry

All ACT Math Resources

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