Question

BC¯¯¯¯¯ is parallel to DE¯¯¯¯¯.

Answer 1

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:

$\dfrac{AC}{AE}=\dfrac{AB}{AD}$

We have AC = x, AE = x + 15, AB = 8, AD = 8 + 10 = 18.

Substitute:

$\dfrac{x}{x+15}=\dfrac{8}{18}$               cross multiply

$18x=8(x+15)$           use distributive property a(b + c) = ab + ac

$18x=8x+120$             subtract 8x from both sides

$10x=120$          divide both sides by 10

$\boxed{x=12}$

Answer: AC = 12