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BC¯¯¯¯¯ is parallel to DE¯¯¯¯¯.

What is AC?



Enter your answer in the box.

BC¯¯¯¯¯ is parallel to DE¯¯¯¯¯. What is AC? Enter your answer in the box.-example-1

1 Answer

3 votes

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

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