Geometry

Question Analysis

This question focuses on applying the properties of isosceles right - triangles to determine the missing side lengths. The key lies in using the relationships between the legs and the hypotenuse of such triangles.

 

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 , 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. Find the length of side :

Given that one leg of the isosceles right - triangle is . Since the two legs of an isosceles right - triangle are equal, .

2. Find the length of side :

Using the formula , substitute . Then

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