Geometry

Question Analysis

This question focuses on leveraging the properties of isosceles right - triangles. The key task is to use the relationship 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. 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 isosceles right - triangle, the hypotenuse , and the unknown side  is a leg.

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

We know the formula , where  and .

Rearranging the formula to solve for , we get

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