Question

Triangle A has sides of lengths `12 ,1 4`, and `11`. Triangle B is similar to triangle A and has a side of length `4`. What are the possible lengths of the other two sides of triangle B?

Answer 1

the other two sides are: 1) `14/3 and 11/3` or 2) `24/7` and `22/7` or 3) `48/11` and `56/11`

Explanation:

Since B and A are similar their sides are in the following possible ratios:

`4/12 or 4/14 or 4/11`

1) ratio`=4/12=1/3`: the other two sides of A are `14*1/3=14/3` and `11*1/3=11/3`

2) ratio`=4/14=2/7`: the other two sides are `12*2/7=24/7` and `11*2/7=22/7`

3) ratio`=4/11`: the other two sides are `12*4/11=48/11` and `14*4/11=56/11`