Answer:
[tex]MG=56\ units[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem we have that
∆EGF~∆EML
so
[tex]\frac{EG}{EM}=\frac{EF}{EL}[/tex]
substitute the given values
[tex]\frac{5x+2}{16}=\frac{126}{28}[/tex]
solve for x
[tex]5x+2=\frac{126}{28}(16)[/tex]
[tex]5x+2=72\\5x=70\\x=14[/tex]
[tex]EG=5x+2=5(14)+2=72\ units[/tex]
step 2
Find MG
we know that
[tex]MG=EG-EM[/tex]
substitute
[tex]MG=72-16=56\ units[/tex]
