Mock AIME 4 2006-2007 Problems/Problem 11
Problem
Let be an equilateral triangle. Two points
and
are chosen on
and
, respectively, such that
. Let
be the intersection of
and
. The area of
is 13 and the area of
is 3. If
, where
,
, and
are relatively prime positive integers, compute
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Let , and
. Note that we want to compute the ratio
.
Assign a mass of to point
. This gives point
a mass of
and point
a mass of
. Thus,
.
Since the ratio of areas of triangles that share an altitude is simply the ratio of their bases, we have that:
.
By the quadratic formula, we find that , so
.
Thus, our final answer is .