Question

3. Find the length of MG. EGF ~ EML.

Answer 1

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= $\frac{EM}{EG} =\frac{EL}{EF} =\frac{ML}{GF} .$

$\frac{16}{5x+2}=\frac{28}{126}$.

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.