2014 AMC 12B Problems/Problem 21
Problem 21
In the figure, is a square of side length
. The rectangles
and
are congruent. What is
?
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