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4 years ago

Given EGF~HGI what is the value of x

Mathematics

1 answer:

saveliy_v [14]4 years ago

8 0

Answer:

$x = 14$

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

$\frac{FG}{GI} = \frac{EG}{GH}$

$\frac{x + 4}{30} = \frac{12}{20}$

Cross multiply

$(x + 4)(20) = (12)(30)$

$20x + 80 = 360$

Subtract 80 from both sides

$20x + 80 - 80 = 360 - 80$

$20x = 280$

Divide both sides by 20

$\frac{20x}{20} = \frac{280}{20}$

$x = 14$

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