Question

Triangle A has sides of lengths `12 ,1 4`, 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 other two sides are
Case 1 : 10.5, 8.25
Case 2 : 7.7143, 7.0714
Case 3 : 9.8182, 11.4545

Explanation:

Triangles A & B are similar.
Case (1)
`:.9/12=b/14=c/11`
`b=(9*14)/12= 10.5`
`c=(9*11)/12= 8.25`

Possible lengths of other two sides of triangle B are
`9, 10.5, 8.25`

Case (2)
`:.9/14=b/12=c/11`
`b=(9*12)/14=7.7143`
`c=(9 * 11)/14=7.0714`

Possible lengths of other two sides of triangle B are
`9, 7.7143, 7.0714`

Case (3)
`:.9 /11=b/12=c/14`
`b=(9*12)/11=9.8182`
`c=(9*14)/11=11.4545`

Possible lengths of other two sides of triangle B are
`8, 9.8182, 11.4545`