How to find the length of the diagonal of a quadrilateral

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

Questions 1 - 3

1

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

$3x\sqrt2$

$3\sqrt2$

$3x^2\sqrt2$

$3\sqrt{2x}$

$9x\sqrt2$

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.

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

2

If the rectangle has side lengths of and , what is the diagonal of the rectangle?

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

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

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

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

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

Explanation

Use the Pythagorean Theorem to solve for the diagonal.

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

3

Q12

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

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.

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

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

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