Question

Triangle A has sides of lengths `27`, `12`, and `21`. Triangle B is similar to triangle A and has a side of length `3`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible lengths of the triangle B are

Case (1)
`3, 5.25, 6.75`

Case (2)
`3, 1.7, 3.86`

Case (3)
`3, 1.33, 2.33`

Explanation:

Triangles A & B are similar.
Case (1)
`:.3/12=b/21=c/27`
`b=(3*21)/12= 5.25`
`c=(3*27)/12= 6.75`

Possible lengths of other two sides of triangle B are
`3, 5.25, 7.75`

Case (2)
`:.3/21=b/12=c/27`
`b=(3*12)/21=1.7`
`c=(3*27)/21=3.86`

Possible lengths of other two sides of triangle B are
`3, 1.7, 3.86`

Case (3)
`:.3/27=b/12=c/21`
`b=(3*12)/27=1.33`
`c=(3*21)/27=2.33`

Possible lengths of other two sides of triangle B are
`3, 1.33, 2.33`