Question

find x - the length of the hypotenuse of the triangle.

Explanation:

Step1: Identify the type of triangle

This is a \(45 - 45-90\) right - triangle. In a \(45 - 45-90\) triangle, the legs are equal in length. Let the length of each leg be \(a\). Here \(a = 5\).

Step2: Use the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). In a \(45 - 45-90\) triangle (\(a = b\)), if \(a=b = 5\), then \(c^{2}=5^{2}+5^{2}\).

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Answer:

\(5\sqrt{2}\)