Question

What is the value of x? Enter your answer, as a decimal, in numerical value only.

Answer 1

x = 67.5

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

`(MA)/(AN)` =
`(MB)/(BP)` ( substitute values )

`(71.5-22)/(22)` =
`(x)/(97.5-x)` , that is

`(49.5)/(22)` =
`(x)/(97.5-x)` ( 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