Answer:
x = 67.5
Step-by-step explanation:
If a line is parallel to a side of a triangle and intersects the other 2 sides , it divides those sides proportionally.
AB is parallel to NP and intersects the other 2 sides , then
[tex]\frac{MA}{AN}[/tex] = [tex]\frac{MB}{BP}[/tex] ( substitute values )
[tex]\frac{71.5-22}{22}[/tex] = [tex]\frac{x}{97.5-x}[/tex] , that is
[tex]\frac{49.5}{22}[/tex] = [tex]\frac{x}{97.5-x}[/tex] ( cross- multiply )
49.5(97.5 - x) = 22x ← distribute left side
4826.25 - 49.5x = 22x ( add 49.5x to both sides )
4826.25 = 71.5x ( divide both sides by 71.5 )
67.5 = x
