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Revision as of 15:15, 10 August 2017
Problem
In the figure, the length of side of square is and =1. What is the area of the inner square ?
Solution
We see that side , which we know is 1, is also the shorter leg of one of the four right triangles (which are congruent, I'll not prove this). So, . Then , and is one of the sides of the square whose area we want to find. So:
So, the area of the square is .
See Also
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.