Question

Triangle A has sides of lengths `12 ,17`, and `11`. Triangle B is similar to triangle A and has a side of length `9`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible lengths of the triangle B are

Case (1)
`9, 8.25, 12.75`

Case (2)
`9, 6.35, 5.82`

Case (3)
`9, 9.82, 13.91`

Explanation:

Triangles A & B are similar.
Case (1)
`:.9/12=b/11=c/17`
`b=(9*11)/12= 8.25`
#c=(9*17)/12= 12.75

Possible lengths of other two sides of triangle B are
`9, 8.25, 12.75`

Case (2)
`:.9/17=b/12=c/11`
`b=(9*12)/17=6.35`
`c=(9*11)/17=5.82`

Possible lengths of other two sides of triangle B are
`9, 6.35, 5.82`

Case (3)
`:.9/11=b/12=c/17`
`b=(9*12)/11=9.82`
`c=(9*17)/11=13.91`

Possible lengths of other two sides of triangle B are
`9, 9.82, 13.91`