1963 AHSME Problems/Problem 15
Problem
A circle is inscribed in an equilateral triangle, and a square is inscribed in the circle. The ratio of the area of the triangle to the area of the square is:
Solution
Let the radius of the circle be . That means the diameter of the circle is , so the side length of the square is . Therefore, the area of the square is .
By using 30-60-90 triangles, half of the side length of an equilateral triangle is , so each side is units long. Thus, the area of the equilateral triangle is .
The ratio of the area of the equilateral triangle to the area of the square is , so the answer is .
See Also
1963 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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