Mr. Lisa wants to hang a triangular banner at the entrance of the school. He performs an unknown dilation to include the banner labeled ∆A'B'C' on a sketch. If side A'B' is 8 units, what will be the measure of B'C' if the measure of AB is 24 feet and BC is 6 feet?

B'C' = 2 units

Step-by-step explanation:

The dilation performed makes ∆A'B'C' (sketched flag) similar to ∆ABC (actual flag).

Given that, A'B' = 8 units, AB = 24 ft, and BC = 6 ft, therefore:

A'B'/AB = B'C'/BC

Substitute

8/24 = B'C'/6

Cross multiply

24*B'C' = 8*6

24*B'C' = 48

B'C' = 48/24

B'C' = 2 units