Question

Triangle A has sides of lengths `54`, `44`, and `32`. Triangle B is similar to triangle A and has a side of length `4`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Because the problem doesn't state which side in Triangle A corresponds to the side of length 4 in triangle B, there are multiple answers.

If the side with length 54 in A corresponds to 4 in B:

Find the proportionality constant:

`54K=4`
`K =4/54=2/27`

The 2nd side `=2/27 *44=88/27`
The3rd side`=2/27*32=64/27`

If the side with length 44 in A corresponds to 4 in B:

`44K=4`
`K=4/44 = 1/11`

The 2nd side`=1/11*32=32/11`
The 3rd side`=1/11*54=54/11`

If the side with length 32 in A corresponds to 4 in B:

`32K=4`
`K=1/8`

The 2nd side`=1/8 *44=11/2`
The 3rd side`=1/8*54=27/4`