The length of MG is 56 for the given similar triangles.
Step-by-step explanation:
Let us consider EML and EGF is two similar triangles.
From the triangle,
EG=5x+2.
EM=16.
EL=28.
EF=126.
According to similar triangle property,
triangle ratio= [tex]\frac{EM}{EG} =\frac{EL}{EF} =\frac{ML}{GF} .[/tex]
[tex]\frac{16}{5x+2}=\frac{28}{126}[/tex].
126(16)=28(5x+2).
2016=140x+56.
140x=1960.
x=14.
⇒EG=5(14)+2.
EG=70+2.
EG=72.
To find the length of MG,
EG=EM+MG.
MG=EG-EM.
=72-16.
MG=56.
