Question

the hypotenuse of a 45 - 45 - 90° triangle measures 24 inches. what is the length of one of the legs of the triangle? 12 in. 12√2 in. 24 in. 24√2 in.

Explanation:

Step1: Recall 45 - 45 - 90 ratio

In a 45 - 45 - 90 triangle, if hypotenuse is $c$ and legs are $a$ and $b$, $a = b$ and $c=\sqrt{2}a$.

Step2: Solve for leg length

Given $c = 24$, then $a=\frac{c}{\sqrt{2}}=\frac{24}{\sqrt{2}}=\frac{24\sqrt{2}}{2}=12\sqrt{2}$.

Answer:

$12\sqrt{2}\text{ in.}$