2015 AMC 10B Problems/Problem 13
We find the x-intercepts and the y-intercepts to find the intersections of the axes and the line. If , then
. If
is
, then
. Our three vertices are
,
, and
. Two of our altitudes are
and
. Since the area of the triangle is
, our final altitude has to be
divided by the hypotenuse. By the Pythagorean Theorem, our hypotenuse is
, so the sum of our altitudes is
.