Question

What is the value of x?

Answer 1

`x=50.6\ cm`

Explanation:

we have that

Triangle AMB and NMP are similar by AA Similarity Theorem

we know that

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

so

`(AM)/(NM)=(MB)/(MP)`

substitute the given values

`(46.2-14)/(46.2)=(x)/(72.6)`

solve for x

`(32.2)/(46.2)=(x)/(72.6)`

`x=(32.2)/(46.2)(72.6)`

`x=50.6\ cm`