Area intersection

Geometry Level 4

In a A B C \triangle{ABC} take points P P and Q Q in A B AB such that A P = P Q = Q B = 30 AP=PQ=QB=30 and points S S and T T in A C AC such that A S = S T = T C = 40 AS=ST=TC=40 . Intersection of triangle P T B \triangle{PTB} and C Q S \triangle{CQS} has area 640 640 . Find the distance from B B to the line A C AC .


The answer is 45.

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