2010 AMC 12B Problems/Problem 13
Problem
In ,
and
. What is
?
Solution
We note that
and
.
Therefore the only way to satisfy the equation is if both
and
, since if either one of these is less than 1, the other one would have to be greater than 1, which our previous statement.
From this we can easily deduce that
and
(since
and
) and solving this system gives us
and
. It is obvious from this that
is a
triangle, and solving for the sides gives us