Problem 48
Question
Find the length of the sides of a regular hexagon inscribed in a circle of radius 25 inches.
Step-by-Step Solution
Verified Answer
The length of the sides of the regular hexagon is 25 inches.
1Step 1: Draw a diagram
It's useful to start with a diagram. Draw a circle with a regular hexagon inscribed inside. Draw lines from the center of the hexagon to each of the vertices. This divides the hexagon into six equal equilateral triangles.
2Step 2: Examine one of the triangles
Focus on one of these triangles. It's an equilateral triangle (all sides and angles are equal), so the angle at the center of the hexagon is 60 degrees. We also know the length of one side - it's the radius of the circle, which is given as 25 inches.
3Step 3: Identify the side length
Since all sides of an equilateral triangle are of equal length, the length of a side of the hexagon is the same as the length of the radius of the circle. Therefore, the length of one side of the hexagon is also 25 inches.
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