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 ratios

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

Step2: Solve for leg length

Given hypotenuse \(= 24\) inches, so \(x\sqrt{2}=24\). 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.)