Geometry

Question Analysis

This question is centered around applying the properties of isosceles right - triangles (45 - 45 - 90 triangles) to find the length of the legs when the hypotenuse length is provided. The main focus is using the relationship between the legs and the hypotenuse of such triangles.

 

Key Concept Explanation

In a 45 - 45 - 90 triangle, the two legs are of equal length. Let the length of each leg be  and the length of the hypotenuse be . From the Pythagorean theorem (, with  in this case), we get . The relationship between the leg and the hypotenuse is , which can be rearranged to .

 

Step - by - Step Solution

1. Substitute the hypotenuse value into the formula:

Given that  cm. Using the formula , we substitute  into it. So, .

2. Simplify the expression:

When dividing b...