Geometry

Question Analysis

This question focuses on applying the properties of isosceles right - triangles to find the missing side lengths. The key is to use the relationships between the legs and the hypotenuse of an isosceles right - 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. Find the length of side :

Since the triangle is an isosceles right - triangle and one leg is , and the two legs are equal in length, then .

2. Find the length of side :

Using the formula , where