Question

A problem is attached

Answer 1

by symmetry, the two triangles AMP and NPB will have the same dimensions. thus NB=3 and AM=5. any deviations in the line will increase the area of the triangle that increases by a larger amount than the decrease in area of the triangle that decreases (a diagram might help here)

this can also be done formally using calculus:
tan(theta)=5/(x-3) (for the inner triangle)
area=x^2*tan(theta)/2 (for the outer triangle)
area=5x^2/(2*(x-3))
set area'(x)=0 and solve, yielding x=6 as expected

Answer 2

geometrically, AMP will be similar to PNB