Geometry

Question Analysis

This question focuses on applying the properties of isosceles right - triangles (45 - 45 - 90 triangles) to find the length of the legs when the hypotenuse is given. The key is to use 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 . 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. Use the formula for the leg of a 45 - 45 - 90 triangle:

Given that  cm. We use the formula .

Substitute  into the formula:

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