Question

Triangle A has sides of lengths `12 ,17`, and `11`. Triangle B is similar to triangle A and has a side of length `8`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible lengths of other two sides of triangle B are
Case 1 : 11.3333, 7.3333
Case 2 : 5.6471, 5.1765
Case 3 : 8.7273, 12.3636

Explanation:

Triangles A & B are similar.
Case (1)
`:.8/12=b/17=c/11`
`b=(8*17)/12= 11.3333`
`c=(8*11)/12= 7.3333`

Possible lengths of other two sides of triangle B are
`8, 11.3333, 7.3333`

Case (2)
`:.8/17=b/12=c/11`
`b=(8*12)/17=5.6471`
`c=(8*11)/17=5.1765`

Possible lengths of other two sides of triangle B are
`8, 7.3333, 5.1765`

Case (3)
`:.8/11=b/12=c/17`
`b=(8*12)/11=8.7273`
`c=(8*17)/11=12.3636`

Possible lengths of other two sides of triangle B are
`8, 8.7273, 12.3636`