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

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

A square has a length of . What must be the length of the diagonal?

Possible Answers:

$3x^2\sqrt2$

$9x\sqrt2$

$3x\sqrt2$

$3\sqrt{2x}$

$3\sqrt2$

Correct answer:

$3x\sqrt2$

Explanation:

A square with a length of indicates that all sides are since a square has 4 equal sides. Use the Pythagorean Theorem to solve for the diagonal.

a^2+b^2=c^2

$c=\sqrt{a^2+b^2} = \sqrt{(3x)^2+(3x)^2}= \sqrt{9x^2+9x^2}= \sqrt{18x^2}= 3x\sqrt2$

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Example Question #2 : How To Find The Length Of The Diagonal Of A Quadrilateral

If the rectangle has side lengths of x+3 and x+4 , what is the diagonal of the rectangle?

Possible Answers:

$\sqrt{2x^2+14x+25}$

$\sqrt{2x^2+5}$

$\sqrt{2x^2+14x+24}$

$x+\frac{7}{3}$

$\sqrt{x^2+7x+12}$

Correct answer:

$\sqrt{2x^2+14x+25}$

Explanation:

Use the Pythagorean Theorem to solve for the diagonal.

a^2+b^2=c^2

(x+3)^2+(x+4)^2=c^2

c^2 = (x^2+6x+9) + (x^2+8x+16) = 2x^2+14x+25

$c=\sqrt{2x^2+14x+25}$

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Example Question #3 : How To Find The Length Of The Diagonal Of A Quadrilateral

Q12

In the parallelogram above, $\overline{CE}=\frac{3x}{2}$ and $\overline{EB}=2x-2$ . What is the length of the diagonal $\overline{CB}$ ?

Possible Answers:

Correct answer:

Explanation:

In a parallelogram, the two diagonals bisect each other at their centers. Therefore, $\overline{CE}=\overline{EB}$ . To find , we set them equal to one another and solve.

$\frac{3x}{2}=2x-2$

3x=2(2x-2)=4x-4

x=4

Plugging this value back into both equations, then adding those values together, gives us our answer of .

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

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

Example Question #2 : How To Find The Length Of The Diagonal Of A Quadrilateral

Example Question #3 : How To Find The Length Of The Diagonal Of A Quadrilateral

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