Question

What is the value of x? Enter your answer, as a decimal, in the box. m Triangle M N P with segment A B parallel to segment N P and A is between M and N and B is between M and P. M N equals 67.2 meters, A N equals 32 meters, M P equals 81.9 meters, and M B equals x.

Answer 1

Answer:

$x=42.9\ m$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two figures are similar, the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles MNP and MAB are similar by AA Similarity Theorem

so

$\frac{MA}{MN}=\frac{MB}{MP}$

we have

$MA=MN-AN=67.2-32=35.2\ m$

$MN=67.2\ m$

$MB=x\ m$

$MP=81.9\ m$

substitute the given values

$\frac{35.2}{67.2}=\frac{x}{81.9}$

Solve for x

$x=\frac{35.2}{67.2}(81.9)\\\\x=42.9\ m$