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
