2013 AIME I Problems/Problem 3
It's important to note that is equivalent to
We define as the length of the side of larger inner square, which is also
,
as the length of the side of the smaller inner square which is also
, and
as the side length of
. Since we are given that the sum of the areas of the two squares is
of the the area of ABCD, we can represent that as
. The sum of the two nonsquare rectangles can then be represented as
.
Looking back at what we need to find, we can represent as
. We have the numerator, and dividing
by two gives us the denominator
. Dividing
gives us an answer of
.