Geometry

Question Analysis

This question focuses on applying the properties of isosceles right - triangles. The main task is to use the relationships between the sides of an isosceles right - triangle to find the value of the unknown side .

 

Key Concept Explanation

In an isosceles right - triangle, the two legs are of equal length, and the hypotenuse  and leg  are related by the formula . This is derived from the Pythagorean theorem . Since  in an isosceles right - triangle, we have , which simplifies to , or .

 

Step - by - Step Solution

1. Identify the sides of the isosceles right - triangle:

In the given triangle, the hypotenuse is , and the unknown side  is a leg.

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

We know that , where

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