Answer:
[tex] x = 14 [/tex]
Step-by-step explanation:
Since ∆EGF is similar to ∆HGI, therefore, the ratio of their corresponding side lengths are the same.
Thus, FG:GI = EG:GH
FG = x + 4
GI = 30
EG = 12
GH = 20
[tex] \frac{FG}{GI} = \frac{EG}{GH} [/tex]
[tex] \frac{x + 4}{30} = \frac{12}{20} [/tex]
Cross multiply
[tex] (x + 4)(20) = (12)(30) [/tex]
[tex] 20x + 80 = 360 [/tex]
Subtract 80 from both sides
[tex] 20x + 80 - 80 = 360 - 80 [/tex]
[tex] 20x = 280 [/tex]
Divide both sides by 20
[tex] \frac{20x}{20} = \frac{280}{20} [/tex]
[tex] x = 14 [/tex]
