Geometry

Question Analysis

This question is about using the properties of isosceles right - triangles (45 - 45 - 90 triangles) to determine the length of the legs when the hypotenuse is known. The core 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 . From the Pythagorean theorem (, with  here), we get , and the formula for the relationship between the leg and the hypotenuse is , which can be rewritten as .

 

Step - by - Step Solution

1. Apply the formula for the leg length:

Given that  cm. We use the formula .

Substitute

Click "Show Answer" to reveal the answer and analysis