Is it a right triangle?

In the triangle ABC, with AB = 5, BC = 3, CA = 4,
a point P is inside the ABC;

two chevians, APD and CPE, make triangle APE
with area equal to half area of the triangle ABC:
area(APE) = 1/2*area(ABC).
Is it possible that angle APE is 90 deg?

Answer is: 'NOT', but better try youself!/

This 'NOT' Answer is NOT correct!
Correct answer is: