Geometry

Question Analysis

This question focuses on using the properties of 30 - 60 - 90 right - triangles to find the lengths of the unknown sides. The key is applying the side - length relationships specific to these triangles.

 

Key Concept Explanation

In a 30 - 60 - 90 right - triangle, if the short leg (opposite the 30° angle) has length , the long leg (opposite the 60° angle) has length , and the hypotenuse (opposite the 90° angle) has length .

 

Step - by - Step Solution

1. Identify the hypotenuse:

Since the side with length  is opposite the 90° angle, it is the hypotenuse. Let the short leg (opposite 30° angle) be . Given that the hypotenuse = 2x, and the hypotenuse is , we solve for  by setting , which gives . So the side .

2. Find the length of the long leg

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