Question

Triangle A has sides of lengths `32`, `48`, and `64`. 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:`32, 48, 64`
Triangle B: `8, 12, 16`
Triangle B:`16/3, 8, 32/3`
Triangle B:`4, 6, 8`

Explanation:

Given Triangle A:`32, 48, 64`
Let triangle B have sides x, y, z then, use ratio and proportion to find the other sides.
If the first side of triangle B is x=8, find y, z

solve for y:

`y/48=8/32`

`y=48*8/32`

`y=12`
```````````````````````````````````````
solve for z:
`z/64=8/32`

`z=64*8/32`
`z=16`
Triangle B: `8, 12, 16`

the rest are the same for the other triangle B

if the second side of triangle B is y=8, find x and z

solve for x:
`x/32=8/48`
`x=32*8/48`
`x=32/6=16/3`

solve for z:
`z/64=8/48`
`z=64*8/48`
`z=64/6=32/3`

Triangle B:`16/3, 8, 32/3`
~~~~~~~~~~~~~~~~~~~~

If the third side of triangle B is z=8, find x and y
`x/32=8/64`
`x=32*8/64`
`x=4`

solve for y:

`y/48=8/64`

`y=48*8/64`
`y=6`

Triangle B:`4, 6,8`

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