2017 AIME I Problems/Problem 15
Problem 15
The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths 
and 
as shown, is 
where 
and 
are positive integers, 
and 
are relatively prime, and is not divisible by the square of any prime. Find 
[asy] size(5cm); pair C=(0,0),B=(0,2*sqrt(3)),A=(5,0); real t = .385, s = 3.5*t-1; pair R = A*t+B*(1-t), P=B*s; pair Q = dir(-60) * (R-P) + P; fill(P--Q--R--cycle,gray); draw(A--B--C--A^^P--Q--R--P); dot(A--B--C--P--Q--R); [/asy]
