Question

The figure shows
△
A
B
E
and
△
A
C
D
, with
¯¯¯¯¯¯
B
E
∥
¯¯¯¯¯¯
C
D
.

Triangle A-C-D with point B on side A-C and point E on side A-D. B is connected to E forming a triangle A-B-E. A-B is 12, B-C is 8 and B-E is 24.

What is the length of
¯¯¯¯¯¯
C
D
?

A.
16

B.
32

C.
36

D.
40

Answer 1

Because BE ∥ CD, triangles ABE and ACD are similar. Corresponding sides give

BE/CD = AB/AC.

AC = AB + BC = 12 + 8 = 20, so

CD = BE · (AC/AB) = 24 · (20/12) = 24 · (5/3) = 40.

Answer: D (40).