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: Recall the property of a 45° - 45° - 90° triangle

In a 45° - 45° - 90° triangle, if the length of each leg is \(a\) and the length of the hypotenuse is \(c\), then \(c = a\sqrt{2}\).

Step2: Solve for \(a\)

Given \(c = 10\sqrt{5}\), from \(c = a\sqrt{2}\), we have \(a=\frac{c}{\sqrt{2}}\). Substitute \(c = 10\sqrt{5}\) into the formula:

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Answer:

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