1987 AHSME Problems/Problem 21
Problem
There are two natural ways to inscribe a square in a given isosceles right triangle. If it is done as in Figure 1 below, then one finds that the area of the square is . What is the area (in ) of the square inscribed in the same as shown in Figure 2 below?
Solution
We are given that the area of the inscribed square is , so the side length of that square is . Since the square divides the larger triangle into 2 smaller congruent , then the legs of the larger isosceles right triangle ( and ) are equal to .
We now have that , so . But we want the area of the square which is
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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