Answer:
MG = 56
Step-by-step explanation:
The triangles EML and EGF are similar thus the ratios of corresponding sides are equal, that is
[tex]\frac{EM}{EG}[/tex] = [tex]\frac{EL}{EF}[/tex] , and substituting values
[tex]\frac{16}{5x+2}[/tex] = [tex]\frac{28}{126}[/tex] ( cross- multiply )
28(5x + 2) = 2016 ( divide both sides by 28 )
5x + 2 = 72 ( subtract 2 from both sides )
5x = 70 ( divide both sides by 5 )
x = 14
Thus
EG = 5x + 2 = 5(14) + 2 = 70 + 2 = 72
Hence
MG = EG - EM = 72 - 16 = 56
