Question

Triangle A has an area of `3` and two sides of lengths `5` and `6`. Triangle B is similar to triangle A and has a side with a length of `11`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Min Possible Area = `10.083`
Max Possible Area = `14.52`

Explanation:

When two objects are similar, their corresponding sides form a ratio. If we square the ratio, we get the ratio related to area.

If triangle A's side of 5 corresponds with triangle B's side of 11, it creates a ratio of `5/11`.
When squared, `(5/11)^2 = 25/121` is the ratio related to Area.

To find the Area of Triangle B, setup a proportion:
`25/121 = 3/(Area)`
Cross Multiply and Solve for Area:
`25(Area) = 3(121)`
`Area = 363/25 = 14.52`

If triangle A's side of 6 corresponds with triangle B's side of 11, it creates a ratio of `6/11`.
When squared, `(6/11)^2 = 36/121` is the ratio related to Area.

To find the Area of Triangle B, setup a proportion:
`36/121 = 3/(Area)`
Cross Multiply and Solve for Area:
`36(Area) = 3(121)`
`Area = 363/36 = 10.083`

So Minimum Area would be 10.083
while Maximum Area would be 14.52