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.
(image of a right triangle with two 45° angles, hypotenuse labeled 24 in.)

Explanation:

Step1: Recall 45-45-90 triangle ratios

In a \(45^\circ - 45^\circ - 90^\circ\) triangle, the ratio of leg : leg : hypotenuse is \(1:1:\sqrt{2}\). Let the length of each leg be \(x\), then hypotenuse \(h = x\sqrt{2}\).

Step2: Solve for leg length

Given hypotenuse \(h = 24\) inches, we have \(x\sqrt{2}=24\). Solve for \(x\): \(x=\frac{24}{\sqrt{2}}\). Rationalize the denominator: \(x = \frac{24\sqrt{2}}{2}=12\sqrt{2}\) inches.

Answer:

\(12\sqrt{2}\) in. (corresponding to the option: \(12\sqrt{2}\) in.)