Geometry

Question Analysis

This question focuses on using the properties of isosceles right - triangles. The main task is to determine the value of the unknown side  by applying the relationship between the sides of such a triangle.

 

Key Concept Explanation

In an isosceles right - triangle, the two legs are of equal length. Let the length of each leg be  and the length of the hypotenuse be . According to the Pythagorean theorem (, and since  in an isosceles right - triangle, ), the relationship between the leg and the hypotenuse is .

 

Step - by - Step Solution

1. Identify the sides of the triangle:

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

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

Using the formula , where  and .

Rearrange the formula to solve for :

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