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 the ratio of sides in a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the legs are of equal length \(x\) and the hypotenuse \(c = x\sqrt{2}\).

Step2: Solve for \(x\) (the length of the leg)

Given \(c = 24\) inches. Using the formula \(c=x\sqrt{2}\), we can solve for \(x\) by \(x=\frac{c}{\sqrt{2}}\).
Rationalize the denominator: \(x=\frac{24}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{24\sqrt{2}}{2}=12\sqrt{2}\) inches.

Answer:

\(12\sqrt{2}\text{ in}\) (the second option).