Question

Triangle A has sides of lengths `12`, `9`, and `8`. 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

The other two sides of triangle are
Case 1 : 12, 10.6667
Case 2 : 21.3333, 14.2222
Case 3 : 24, 18

Explanation:

Triangles A & B are similar.
Case (1)
`:.16/12=b/9=c/8`
`b=(16*9)/12= 12`
`c=(16*8)/12= 10.6667`

Possible lengths of other two sides of triangle B are
`9, 12, 10.6667`

Case (2)
`:.16/9=b/12=c/8`
`b=(16*12)/9=21.3333`
`c=(16 * 8)/9=14.2222`

Possible lengths of other two sides of triangle B are
`9, 21.3333, 14.2222`

Case (3)
`:.16 /8=b/12=c/9`
`b=(16*12)/8=24`
`c=(16*9)/8=18`

Possible lengths of other two sides of triangle B are
`8, 24, 18`