Question

Triangle A has sides of lengths `36 ,24`, and `16`. Triangle B is similar to triangle A and has a side of length `8`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Triangle A: 36, 24, 16
Triangle B: `8,16/3,32/9`
Triangle B: `12, 8, 16/3`
Triangle B: `18, 12, 8`

Explanation:

From the given
Triangle A: 36, 24, 16

Use ratio and proportion

Let x, y, z be the sides respectively of triangle B proportional to triangle A

Case 1.

If x=8 in triangle B, solve y
`y/24=x/36`

`y/24=8/36`
`y=24*8/36`
`y=16/3`

If x=8 solve z
`z/16=x/36`
`z/16=8/36`
`z=16*8/36`
`z=32/9`
~~~~~~~~~~~~~~~~~~~~~~~
Case 2.

if y=8 in triangle B solve x
`x/36=y/24`
`x/36=8/24`
`x=36*8/24`
`x=12`

If y=8 in triangle B solve z
`z/16=y/24`
`z/16=8/24`
`z=16*8/24`
`z=16/3`
~~~~~~~~~~~~~~~~~~~~~~~
Case 3.

if z=8 in triangle B, solve x
`x/36=z/16`
`x/36=8/16`
`x=36*8/16`
`x=18`

if z=8 in triangle B, solve y
`y/24=z/16`
`y/24=8/16`
`y=24*8/16`
`y=12`

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