If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore
ΔABC is similar to ΔADE.
The sides of smaller triangle are in proportion with sides of bigger triangle.
Therefore we have the equation:
[tex]\dfrac{AC}{AE}=\dfrac{AB}{AD}[/tex]
We have AC = x, AE = x + 15, AB = 8, AD = 8 + 10 = 18.
Substitute:
[tex]\dfrac{x}{x+15}=\dfrac{8}{18}[/tex] cross multiply
[tex]18x=8(x+15)[/tex] use distributive property a(b + c) = ab + ac
[tex]18x=8x+120[/tex] subtract 8x from both sides
[tex]10x=120[/tex] divide both sides by 10
[tex]\boxed{x=12}[/tex]
Answer: AC = 12
