How do you find the diagonal of a rectangle whose sides are 20 and 48?

Apr 21, 2018

See a solution process below:

Explanation:

The corners of a rectangle are right angles. Therefore, we can find the diagonal of a rectangle using the Pythagorean Theorem where the sides of the rectangle are the sides of the right triangle and the diagonal is the hypotenuse.

The Pythagorean Theorem states:

${a}^{2} + {b}^{2} = {c}^{2}$ where $a$ and $b$ are the sides of the right triangle and $c$ is the hypotenuse of the right triangle.

Substituting for $a$ and $b$ and solving for $c$ gives:

${20}^{2} + {48}^{2} = {c}^{2}$

$400 + 2304 = {c}^{2}$

$2704 = {c}^{2}$

$\sqrt{2704} = \sqrt{{c}^{2}}$

$52 = c$

$c = 52$

The diagonal of the rectangle would be 52 units.