Question

Triangle A has sides of lengths `36`, `45`, and `33`. Triangle B is similar to triangle A and has a side of length `7`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible lengths of the triangle B are

Case (1)
`7, 7.64, 9.55`

Case (2)
`7, 6.42, 8.75`

Case (3)
`7, 5.13, 5.6`

Explanation:

Triangles A & B are similar.
Case (1)
`:.7/33=b/36=c/45`
`b=(7*36)/33= 7.64`
`c=(7*45)/33= 9.55`

Possible lengths of other two sides of triangle B are
`7, 7.64, 9.55`

Case (2)
`:.7/36=b/33=c/45`
`b=(7*33)/36=6.42`
`c=(7*45)/36=8.75`

Possible lengths of other two sides of triangle B are
`7, 6.42, 8.75`

Case (3)
`:.7/45=b/33=c/36`
`b=(7*33)/45=5.13`
`c=(7*36)/45=5.6`

Possible lengths of other two sides of triangle B are
`7, 5.13, 5.6`