Question

Triangle A has sides of lengths `81`, `45`, and `66`. 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

Length of other two sides are
Case 1 : 3.8889, 5.7037
Case 2 : 12.6, 10.2667
Case 3 : 4.7727, 8.5909

Explanation:

Triangles A & B are similar.
Case (1)
`:.7/81=b/45=c/66`
`b=(7*45)/81= 3.8889`
`c=(7*66)/81= 5.7037`

Possible lengths of other two sides of triangle B are
`7, 3.8889, 5.7037`

Case (2)
`:.7/45=b/81=c/66`
`b=(7*81)/45=12.6`
`c=(7*66)/45=10.2667`

Possible lengths of other two sides of triangle B are
`7, 12.6, 10.2667`

Case (3)
`:.7/66=b/45=c/81`
`b=(7*45)/66=4.7727`
`c=(7*81)/66=8.5909`

Possible lengths of other two sides of triangle B are
`7, 4.7727, 8.5909`