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 key lies in leveraging the established 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 . By the Pythagorean theorem (, with  in this case), we have . The relationship between the leg and the hypotenuse can be written as , 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

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