Question

Triangle A has sides of lengths `2 ,3`, and `4`. 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

Triangle `1:" " 5, 15/2, 10`
Triangle `2:" " 10/3, 5, 20/3`
Triangle `3:" " 5/2, 15/4, 5`

Explanation:

Given : triangle A: sides 2, 3, 4, use ratio and proportion to solve for the possibles sides

For example: Let the other sides of triangle B represented by x, y,z
If `x=5` find y

`y/3=x/2`

`y/3=5/2`

`y=15/2`

solve for z:

`z/4=x/2`
`z/4=5/2`
`z=20/2=10`

that completes triangle 1:

For triangle `1:" "5, 15/2, 10`

use scale factor `=5/2` to obtain the sides `5, 15/2, 10`

Triangle `2:" " 10/3, 5, 20/3`

use scale factor `=5/3` to obtain the sides `10/3, 5, 20/3`

Triangle `3:" " 5/2, 15/4, 5`
use scale factor `=5/4` to obtain the sides `5/2, 15/4, 5`

God bless...I hope the explanation is useful.