Question

Triangle A has sides of lengths `7 ,4`, and `5`. Triangle B is similar to triangle A and has a side of length `3`. What are the possible lengths of the other two sides of triangle B?

Answer 1

A: Possible lengths of other two sides are `3 3/4 , 5 1/4`
B: Possible lengths of other two sides are `2 2/5 , 4 1/5`
C.Possible lengths of other two sides are `1 5/7 , 2 1/7`

Explanation:

Side lengths of Triangle `A` are `4 ,5 ,7` according to size

A:
When side length `s=3` is smallest in similar triangle `B`

Then middle side length is `m=5*3/4=15/4=3 3/4`

Then largest side length is `m=7*3/4=21/4 = 5 1/4`

Possible lengths of other two sides are `3 3/4 , 5 1/4`

B:
When side length `s=3` is middle one in similar triangle `B`

Then smallest side length is `m=4*3/5=12/5=2 2/5`

Then largest side length is `m=7*3/5=21/5 = 4 1/5`

Possible lengths of other two sides are `2 2/5 , 4 1/5`

C:
When side length `s=3` is largest one in similar triangle `B`

Then smallest side length is `m=4*3/7=12/7=1 5/7`

Then middle side length is `m=5*3/7=15/7 = 2 1/7`

Possible lengths of other two sides are `1 5/7 , 2 1/7`

A: Possible lengths of other two sides are `3 3/4 , 5 1/4` units
B: Possible lengths of other two sides are `2 2/5 , 4 1/5` units
C.Possible lengths of other two sides are `1 5/7 , 2 1/7` units
[Ans]