Question

Triangle A has sides of lengths `42 ,36`, and `21`. Triangle B is similar to triangle A and has a side of length `14`. What are the possible lengths of the other two sides of triangle B?

Answer 1

The possible length of sides for triangle B are `{14,12,7}`, `{14,49/3,49/6}`,`{14,28,24}`

Explanation:

Let say 14 is a length of triangle B reflect to the length of 42 for triangle A and X,Y are the length for other two sides of triangle B.

`X/36 = 14/42`
`X=14/42*36`
`X=12`

`Y/21 = 14/42`
`Y=14/42*21`
`Y=7`
The length of sides for triangle B are `{14,12,7}`

Let say 14 is a length of triangle B reflect to the length of 36 for triangle A and X,Y are the length for other two sides of triangle B.
`X/42 = 14/36`
`X=14/36*42`
`X=49/3`

`Y/21 = 14/36`
`Y=14/36*21`
`Y=49/6`
The length of sides for triangle B are `{14,49/3,49/6}`

Let say 14 is a length of triangle B reflect to the length of 21 for triangle A and X,Y are the length for other two sides of triangle B.
`X/42 = 14/21`
`X=14/21*42`
`X=28`

`Y/36 = 14/21`
`Y=14/21*36`
`Y=24`
The length of sides for triangle B are `{14,28,24}`