Question

Triangle A has sides of lengths `12 ,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

Three possibilities are there. Three sides are either (A) `8, 16` and `10 2/3` or (B) `4, 8` and `5 1/3` or (C) `6, 12` and `8`.

Explanation:

The sides of triangle A are `12, 24` and `16` and triangle B is similar to triangle A with a side of length `8`. Let other two sides be `x` and `y`. Now, we have three possibilities. Either

`12/8=24/x=16/y` then we have `x=16` and `y=16xx8/12=32/3=10 2/3` i.e. three sides are `8, 16` and `10 2/3`

or `12/x=24/8=16/y` then we have `x=4` and `y=16xx8/24=16/3=5 1/3` i.e. three sides are `4, 8` and `5 1/3`

or `12/x=24/y=16/8` then we have `x=6` and `y=12` i.e. three sides are `6, 12` and `8`