A rectangular desk is 18 inches by 24 inches. What is the diagonal measurement?

Feb 13, 2017

The diagonal measurement of the desk is 30 inches

Explanation:

Because the corner of a rectangular desk and the diagonal form a right triangle with the diagonal as the hypotenuse and each side of the desk one of the legs of the triangle we can use the Pythagorean Theorem to solve this problem.

The Pythagorean Theorem states:

${a}^{2} + {b}^{2} = {c}^{2}$

Where:

$a$ and $b$ are the sides of the triangle, or, in this case the edges of the desk.

$c$ is the hypotenuse, or, in this case the diagonal of the desk

Substituting the length of the desk edges for $a$ and $b$ and then solving for $c$ gives:

${18}^{2} + {24}^{2} = {c}^{2}$

$324 + 576 = {c}^{2}$

$900 = {c}^{2}$

$\sqrt{900} = \sqrt{{c}^{2}}$

$30 = c$

$c = 30$