Question

Triangle A has an area of `9` and two sides of lengths `6` and `4`. Triangle B is similar to triangle A and has a side of length `15`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area of `Delta B = 126.5625`
Minimum area of `Delta B = 56.25`

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 15 of `Delta B` should correspond to side 4 of `Delta A`.

Sides are in the ratio 15 : 4
Hence the areas will be in the ratio of `15^2 : 4^2 = 225 : 16`

Maximum Area of triangle `B =( 9 * 225) / 16= 126.5625`

Similarly to get the minimum area, side 6 of `Delta A` will correspond to side 15 of `Delta B`.
Sides are in the ratio `15 : 6` and areas `225 : 36`

Minimum area of `Delta B = (9*225)/36= 56.25`