Answer:
[tex]x=50.6\ cm[/tex]
Step-by-step 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
[tex]\frac{AM}{NM}=\frac{MB}{MP}[/tex]
substitute the given values
[tex]\frac{46.2-14}{46.2}=\frac{x}{72.6}[/tex]
solve for x
[tex]\frac{32.2}{46.2}=\frac{x}{72.6}[/tex]
[tex]x=\frac{32.2}{46.2}(72.6)[/tex]
[tex]x=50.6\ cm[/tex]
