Question

BC¯¯¯¯¯ is parallel to DE¯¯¯¯¯.

What is AC?



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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:

`(AC)/(AE)=(AB)/(AD)`

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

Substitute:

`(x)/(x+15)=(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