2014 AMC 12B Problems/Problem 21
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Problem
In the figure, is a square of side length 1. The rectangles
and
are congruent. What is
?
-Insert Diagram because I don't know how-
Solution
Let . Let
. Because
and
,
are all similar. Using proportions and the pythagorean theorem, we find
Because we know that
, we can set up a systems of equations
Solving for
in the second equation, we get
Plugging this into the first equation, we get
Plugging into the previous equation with
, we get