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 property of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the hypotenuse \(c\) is related to the leg \(a\) (or \(b\)) by the formula \(c = a\sqrt{2}\) (since \(a = b\)).

Step2: Solve for the leg length

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

Answer:

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