Question

Triangle A has sides of lengths `48 ,36`, and `54`. Triangle B is similar to triangle A and has a side of length `5`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible sides of `triangleB`:
`color(white)("XXX"){5, 3 3/4, 5 5/8}` or
`color(white)("XXX"){6 2/3, 5, 7 1/2}` or
`color(white)("XXX"){4 4/9, 3 1/3, 5}`

Explanation:

Suppose the sides of `triangleA` are
`color(white)("XXX")P_A=48, Q_A=36, and R_A=54`
with corresponding sides of `triangleB`:
`color(white)("XXX")P_B, Q_B, and R_B`

#{: ("Given:",,,,,), (,P_A,color(white)("xx"),Q_A,color(white)("xx"),R_A), (,48,color(white)("xx"),36,color(white)("xx"),54), ("Possibilities:",,,,,), (,P_B,color(white)("xx"),Q_B,color(white)("xx"),R_B), (,5,color(white)("xx"),5/48 * 36=3 3/4,color(white)("xx"),5/48*54=5 5/8), ("or",5/36 * 48=6 2/3,color(white)("xx"),5,color(white)("xx"),5/36*54=7 1/2), ("or",5/54*48=4 4/9,color(white)("xx"),5/54*36=3 1/3,color(white)("xx"),5) :}#