Question

In the figure above, line segments AD and BE intersect at point C. What is the length of line segment BE?

Possible Answers:
25
30
28
18
20

Answer 1

(a) 25

Explanation:

Given similar triangles ABC and DEC with sides AB=8, BC=10, and DE=12, you want the length of BE.

Similar triangles

Corresponding sides of similar triangles are proportional in length. Here, the corresponding sides are ...

AB : DE = 8 : 12

AC : DC = 6 : __

BC : EC = 10 : __

Solution

Writing the proportion for the side of interest, we get ...

EC/BC= DE/AB

EC/10 = 12/8

Solving for EC gives ...

EC = 10(12/8) = 15

The length of interest is ...

BE = BC +EC = 10 +15

BE = 25