Geometry

Question Analysis

This question focuses on using the properties of 45 - 45 - 90 and 30 - 60 - 90 triangles to find the value of x. The key is correctly applying the side - length relationships of these special triangles.

 

Key Concept Explanation

45 - 45 - 90 triangle: In a 45 - 45 - 90 triangle, if the leg has length , the hypotenuse has length .

30 - 60 - 90 triangle: In a 30 - 60 - 90 triangle, if the side opposite 30° has length , the side opposite 60° has length , and the hypotenuse has length .

 

Step - by - Step Solution

1. Analyze the 45 - 45 - 90 triangle:

The side with length  is the hypotenuse of the 45 - 45 - 90 triangle. Let the leg length be .

Using the formula hypotenuse , we have .

Solve for :

This leg

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