Question

the hypotenuse of a 45° - 45° - 90° triangle measures 10√5 in. what is the length of one leg of the triangle? 5√5 5√10 10√5 10√10

Explanation:

Step1: Define leg length as \( l \)

In 45°-45°-90° triangle, hypotenuse \( h = l\sqrt{2} \)

Step2: Set up equation with given hypotenuse

\( l\sqrt{2} = 10\sqrt{5} \)

Step3: Solve for \( l \)

\( l = \frac{10\sqrt{5}}{\sqrt{2}} = 5\sqrt{10} \)

Answer:

B. \(5\sqrt{10}\)