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?

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

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