Question

What is the value of x?

Enter your answer, as a decimal, in the box.

cm
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 46.2 centimeters, A N equals 14 centimeters, M P equals 72.6 centimeters, and M B equals x.

Answer 1

Value of x is 50.6 cm

Step-by-step explanation:

In the figure attached,

There is a triangle MNP having segment AB parallel to NP.

If AB║NP and MN is a transverse.

Therefore, ∠MAB ≅ ∠MNP [ Corresponding angles]

Similarly If AB║NP and MP is a transverse.

Therefore, ∠MBA ≅ ∠MPN [ Corresponding angles]

By AA property of similarity, ΔMNP and ΔMAB are similar triangle.

And the corresponding sides of these similar triangles will be in the same ratio.

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

$\frac{MN-MA}{MN}=\frac{x}{72.6}$

$\frac{46.2-14}{46.2}=\frac{x}{72.6}$

x = $\frac{32.2\times 72.6}{46.2}$

x = 50.6 cm

Therefore, x = 50.6 is the measure of side MB.

Learn more about the similar triangles from https://brainly.in/question/13227580