examday

/TMUA

A point $P$ lies inside triangle $ABC$.

Through $P$, a line is drawn parallel to $BC$. This line cuts off a smaller triangle at $A$ with area $4$.

Similarly, the line through $P$ parallel to $CA$ cuts off a smaller triangle at $B$ with area $9$, and the line through $P$ parallel to $AB$ cuts off a smaller triangle at $C$ with area $16$.

Each of the three lines is considered separately.

What is the area of triangle $ABC$?