Geometry

Question Analysis

This question focuses on leveraging the properties of isosceles right - triangles. The key task is to utilize the well - known side - length relationships in such triangles to determine the value of the unknown side .

 

Key Concept Explanation

In an isosceles right - triangle, the two legs are of equal length. If the length of each leg is  and the length of the hypotenuse is , then, according to the Pythagorean theorem (, and since  in an isosceles right - triangle, ), we get . This relationship is crucial for solving problems related to the side lengths of isosceles right - triangles.

 

Step - by - Step Solution

1. Identify the sides of the triangle:

In the given isosceles right - triangle, the hypotenuse is , and the side we need to find, , is a leg.

2. Apply the formula for an isosceles right - triangle:

We know the formula , where  and

Click "Show Answer" to reveal the answer and analysis