2014 AMC 12B Problems/Problem 21
Revision as of 21:30, 20 February 2014 by Kevin38017 (talk | contribs) (Created page with "==Problem== In the figure, <math>ABCD</math> is a square of side length 1. The rectangles <math>JKHG</math> and <math>EBCF</math> are congruent. What is <math>BE</math> ? -In...")
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
(Solution by kevin38017)