Question

BC¯¯¯¯¯ is parallel to DE¯¯¯¯¯.

What is AC?



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units

Answer 1

∆ABC ~ ∆ADE

AC/AE = AB/AD

AC = AE•AB/AD

AC = (AC + 15)•8/18

9AC = 4AC + 60

5AC = 60

AC = 12

Answer 2

AC = 12

Explanation:

We can use proportions to solve. Put the smaller triangle side over the larger triangle side

AB AC

--------- = --------

AD AE

Substituting what we know

8 AC

--------- = --------

8+10 AC+15

Using cross products

8 *(AC+15) = (8+10)*AC

Simplify

8 *(AC+15) = (18)*AC

Distribute

8AC +120 = 18AC

Subtract 8AC from each side

8AC-8AC +120 = 18AC -8AC

120 =10AC

Divide each side by 10

120/10 = 10AC/10

12=AC