What is the value of x? enter your answer, as a decimal, in the box. ft 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 71.5 feet, a n equals 22 feet, m p equals 97.5 feet, and m b equals x?

x = 67.5 ft

Explanation:

Following the statements you can draw the triangles mnp and mab.

1) Both are similar triangles with the common vertex m, and with these corresponding sides:

- segment mn corresponding to ma
- segment np corresponding np
- segment mp corresponding mb

2) So, by side-angle-side theorem

segment ma         segment mb
=
segment mn          segment mp

3) You know:

- segment mn = 71.5
- segment ma = 71.5 - 22 = 49.5
- segment mb = x
- segment mp = 97.5

4) Therefore:

    x            49.5
= 
97.5            71.5

5) Solve for x:

x = 97.5 * 49.5 / 71.5 = 67.5

x = 67.5 ft.