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Karolina [17]
3 years ago
8

BC¯¯¯¯¯ is parallel to DE¯¯¯¯¯.

Mathematics
1 answer:
Nuetrik [128]3 years ago
3 0

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}               <em>cross multiply</em>

18x=8(x+15)           <em>use distributive property a(b + c) = ab + ac</em>

18x=8x+120             <em>subtract 8x from both sides</em>

10x=120          <em>divide both sides by 10</em>

\boxed{x=12}

<h2>Answer: AC = 12</h2>
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