Problem
1984 AIME Problem 3
A point P is chosen in the interior of \triangle ABC such that when lines are drawn through P parallel to the sides of \triangle ABC, the resulting smaller triangles t_{1}, t_{2}, and t_{3} in the figure, have areas 4, 9, and 49, respectively. Find the area of \triangle ABC.
![[asy] size(200); pathpen=black+linewidth(0.65);pointpen=black; pair A=(0,0),B=(12,0),C=(4,5); D(A--B--C--cycle); D(A+(B-A)*3/4--A+(C-A)*3/4); D(B+(C-B)*5/6--B+(A-B)*5/6);D(C+(B-C)*5/12--C+(A-C)*5/12); MP("A",C,N);MP("B",A,SW);MP("C",B,SE); /* sorry mixed up points according to resources diagram. */ MP("t_3",(A+B+(B-A)*3/4+(A-B)*5/6)/2+(-1,0.8),N); MP("t_2",(B+C+(B-C)*5/12+(C-B)*5/6)/2+(-0.3,0.1),WSW); MP("t_1",(A+C+(C-A)*3/4+(A-C)*5/12)/2+(0,0.15),ESE); [/asy]](/static/aops/834e3c8f278bbd40bd5596e960fdfda1f0d0b736.png)
Leading zeroes must be inputted, so if your answer is 34, then input 034
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