1962 AHSME Problems/Problem 6
Problem
A square and an equilateral triangle have equal perimeters. The area of the triangle is square inches. Expressed in inches the diagonal of the square is:
Solution
To solve for the perimeter of the triangle we plug in the formula for the area of an equilateral triangle which is . This has to be equal to , which means that , or the side length of the triangle is . Thus, the triangle (and the square) have a perimeter of . It follows that each side of the square is . If we draw the diagonal, we create a 45-45-90 triangle, whose hypotenuse (also the diagonal of the square) is .
See Also
1962 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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