Question

Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides?

A. AC = 6 in.; CE = 18 in.
B. AC = 15 in.; CE = 5 in.
C. AC = 18 in.; CE = 6 in.
D. AC = 5 in.; CE = 15 in.

Answer 1

The answer is gonna be: (B)

Answer 2

Since we have BC ║ DE, we know that:

AB/AD = BC/DE

12/(12 + 4) = BC/12

12/16 = BC/12

BC = (12 · 12)/16 = 9 (in)

Applying the pythagorean, we have:

AB² + BC² = AC²

12² + 9² = AC²

225 = AC²

AC = √225 = 15 (in)

Using the information about the parallel lines again, we have:

AC/CE = AB/BD

15/CE = 12/4

CE = (15 · 4)/12 = 5 (in)

So the answer is B