1984 AIME Problems/Problem 3

Problem

A point $\displaystyle P$ is chosen in the interior of $\displaystyle \triangle ABC$ such that when lines are drawn through $\displaystyle P$ parallel to the sides of $\displaystyle \triangle ABC$ , the resulting smaller triangles $\displaystyle t_{1}$ , $\displaystyle t_{2}$ , and $\displaystyle t_{3}$ in the figure, have areas $\displaystyle 4$ , $\displaystyle 9$ , and $\displaystyle 49$ , respectively. Find the area of $\displaystyle \triangle ABC$ .