Answer:
(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