Question

Triangle A has sides of lengths `36 ,24`, and `27`. Triangle B is similar to triangle A and has a side of length `5`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible lengths of the triangle B are

Case (1)
`5, 5.625, 7.5`

Case (2)
`5, 4.44, 6.67`

Case (3)
`5, 3.33, 3.75`

Explanation:

Triangles A & B are similar.
Case (1)
`:.5/24=b/27=c/36`
`b=(5*27)/24= 5.625`
`c=(5*36)/24= 7.5`

Possible lengths of other two sides of triangle B are
`5, 5.625, 7.5`

Case (2)
`:.5/27=b/24=c/36`
`b=(5*24)/27=4.44`
`c=(5*36)/27=6.67`

Possible lengths of other two sides of triangle B are
`5, 4.44, 6.67`

Case (3)
`:.5/36=b/24=c/27`
`b=(5*24)/36=3.33`
`c=(5*27)/36=3.75`

Possible lengths of other two sides of triangle B are
`5, 3.33, 3.75`