Question

Triangle A has sides of lengths `32`, `24`, and `28`. Triangle B is similar to triangle A and has a side with a length of `16`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible lengths of the triangle B are

Case (1)
`16, 18.67, 21.33`

Case (2)
`16, 13.71, 18.29`

Case (3)
`16, 12, 14`

Explanation:

Triangles A & B are similar.
Case (1)
`:.16/24=b/28=c/32`
`b=(16*28)/24= 18.67`
`c=(16*32)/24= 21.33`

Possible lengths of other two sides of triangle B are
`16, 18.67, 21.33`

Case (2)
`:.16/28=b/24=c/32`
`b=(16*24)/28=13.71`
`c=(16*32)/28=18.29`

Possible lengths of other two sides of triangle B are
`16, 13.71, 18.29`

Case (3)
`:.16/32=b/24=c/28`
`b=(16*24)/32=12`
`c=(16*28)/32=14`

Possible lengths of other two sides of triangle B are
`16, 12, 14`