Geometry

Question Analysis

This question focuses on using the properties of isosceles right - triangles (45 - 45 - 90 triangles) to determine the length of the legs when the hypotenuse is given. The key is to apply the relationship between the legs and the hypotenuse.

 

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 . According to the Pythagorean theorem (, and since  in this triangle, ), 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  cm. Using the formula , we substitute  into it.

So, .

2. Simplify the expression: