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: [tex]\triangle EGF \sim \triangle EML[/tex]
From the given figure:
In [tex]\triangle EGF[/tex] and [tex]\trinagle EML[/tex]
EG = [tex]5x+2[/tex]
EF = [tex]126[/tex]
EM = [tex]16[/tex]
EL = [tex]28[/tex]
By definition of similar triangle,
[tex]\frac{EG}{EM}=\frac{EF}{EL}[/tex] ...... (1)
Substitute the given values in equation (1) as shown below:
[tex]\frac{5x+2}{16}=\frac{126}{28}[/tex]
[tex]5x+2 = 4.5\times 16[/tex]
[tex]5x+2 =72[/tex]
which implies, EG = [tex]72[/tex].
Now to find the value of MG.
EG = EM+MG
[tex]72=16+MG[/tex]
Subtract 16 from both sides, we get
[tex]MG = 56[/tex]
Hence, the value of length of MG = 56.
