1964 AHSME Problems/Problem 10
Problem
Given a square side of length . On a diagonal as base a triangle with three unequal sides is constructed so that its area equals that of the square. The length of the altitude drawn to the base is:
Solution
The area of the square is . The diagonal of a square with side bisects the square into two right triangles, so the diagonal has length .
The area of the triangle is . The base of the triangle is the diagonal of the square, which is . If the area of the triangle is equal to the area of the square, we have:
This is option
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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