Question

Triangle A has sides of lengths `32`, `24`, and `20`. 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

Case (1) 16, 19.2, 25.6
Case (2) 16, 13.3333, 21.3333
Case (3) 16, 10, 12

Explanation:

Triangles A & B are similar.
Case (1)
`:.16/20=b/24=c/32`
`b=(16*24)/20= 19.2`
`c=(16*32)/20= 25.6`

Possible lengths of other two sides of triangle B are
`16, 19.2, 25.6`

Case (2)
`:.16/24=b/20=c/32`
`b=(16*20)/24=13.3333`
`c=(16 * 32)/24=21.3333`

Possible lengths of other two sides of triangle B are
`16, 13.3333, 21.3333`

Case (3)
`:.16 /32=b/20=c/24`
`b=(16*20)/32=10`
`c=(16*24)/32=12`

Possible lengths of other two sides of triangle B are
`16, 10, 12`