Geometry

Question Analysis

This question is about using the properties of isosceles right - triangles (45 - 45 - 90 triangles) to find the length of the legs when the hypotenuse length is given. The main focus is applying 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 ), we get , and the relationship , which can be rewritten as .

 

Step - by - Step Solution

1. Substitute the hypotenuse value into the formula:

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

So, .

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