Question

What is the value of x? Enter your answer, as a decimal, in the box. m Image shows triangle M P N with midsegment A B where A is between M and N and B is between M and P. M N is 80.5 meters. A N is 35 meters. M P is 96.6 meters. M B is x.

Answer 1

Applying BPT theorem in triangle MNP, which states that, If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio.

\frac{MB}{BP}=\frac{MA}{AN}

\frac{x}{96.6-x}=\frac{80.5-35}{35}

\frac{x}{96.6-x}=\frac{45.5}{35}

35x= 45.5(96.6-x)

35x= 4395.3 - 45.5x

80.5x = 4395.3

x=54.6 meters