Question

Triangle A has sides of lengths `32`, `48`, and `36`. 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

The other two sides are 12, 9 respectively.

Explanation:

Since the two triangles are similar, corresponding sides are in the same proportion.
If the `Delta`s are ABC & DEF,
`(AB)/(DE) =( BC)/(EF) = (CA)/(FD)`

`32/8 = 48/(EF) = 36 / (FD)`
`EF = ( 48 * 8)/32 = 12`
`FD = (36 * 8)/ 32 = 9`

Answer 2

The other two sides of triangle `B` could have lengths:

`12` and `9`

`16/3` and `6`

`64/9` and `96/9`

Explanation:

Given triangle A has sides of lengths:

`32, 48, 36`

We can divide all these lengths by `4` to get:

`8, 12, 9`

or by `6` to get:

`16/3, 8, 6`

or by `9/2` to get:

`64/9, 96/9, 8`

So the other two sides of triangle `B` could have lengths:

`12` and `9`

`16/3` and `6`

`64/9` and `96/9`