Question

Find the length of MG. EGF~EML

Answer 1

Answer:

The length of MG = 56.

Step-by-step explanation:

Two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional.

Given that: $\triangle EGF \sim \triangle EML$

From the given figure:

In $\triangle EGF$ and $\trinagle EML$

EG = $5x+2$

EF = $126$

EM = $16$

EL = $28$

By definition of similar triangle,

$\frac{EG}{EM}=\frac{EF}{EL}$                                                           ...... (1)

Substitute the given values in equation (1) as shown below:

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

$5x+2 = 4.5\times 16$

$5x+2 =72$

which implies, EG = $72$.

Now to find the value of MG.

EG = EM+MG

$72=16+MG$

Subtract 16 from both sides, we get

$MG = 56$

Hence, the value of length of MG = 56.