Question

determining leg length in a 45°-45°-90° triangle 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 triangle rule

In a 45°-45°-90° triangle, if leg length is $x$, hypotenuse is $x\sqrt{2}$. Let leg = $x$, hypotenuse = $24$.

Step2: Set up equation and solve for $x$

$$x\sqrt{2}=24$$
$$x=\frac{24}{\sqrt{2}}$$

Step3: Rationalize the denominator

$$x=\frac{24\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{24\sqrt{2}}{2}=12\sqrt{2}$$

Answer:

12√2 in.