Answer :

Answer:

x = 4

Step-by-step explanation:

given Δ EHG and Δ EFD are similar, then the ratios of corresponding sides are in proportion.

EG and ED = x + 5 + 9 = x + 14 are corresponding sides

HG and ED are corresponding sides , then

[tex]\frac{EG}{ED}[/tex] = [tex]\frac{HG}{ED}[/tex] ( substitute values )

[tex]\frac{x+5}{x+14}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex] ( cross multiply )

2(x + 5) = x + 14

2x + 10 = x + 14 ( subtract x from both sides )

x + 10 = 14 ( subtract 10 from both sides )

x = 4