Question

Triangle A has sides of lengths `39`, `45`, and `54`. Triangle B is similar to triangle A and has a side of length `3`. What are the possible lengths of the other two sides of triangle B?

Answer 1

pair 1: x=39, y=45, z=54 and a=13/5, b=3, c=18/5
pair 2: x=39, y=45, z=54 and a=3, b=45/13, c=54/13
pair 3: x=39, y=45, z=54 and a=13/6, b=5/2, c=3

Explanation:

Use ratio and proportion to solve for the sides

First possibility
For triangle A , let sides x=39, y=45, z=54
For triangle B, let sides a=13/5, b=3, c=18/5

second possibility
For triangle A , let sides x=39, y=45, z=54
For triangle B, let sides a=3, b=45/13, c=54/13

third possibility
For triangle A , let sides x=39, y=45, z=54
For triangle B, let sides a=13/6, b=5/2, c=3

God bless...I hope the explanation is useful