2005 AMC 10A Problems/Problem 8
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
.