Question

Triangle A has an area of `27` and two sides of lengths `8` and `6`. Triangle B is similar to triangle A and has a side with a length of `6`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area of `Delt B = 27`
Minimum area of `Delta B = 15.1875`

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 6 of `Delta B` should correspond to side 6 of `Delta A`.

Sides are in the ratio 6 : 6
Hence the areas will be in the ratio of `6^2 : 6^2 = 36 : 36`

Maximum Area of triangle `B =( 27 * 36) / 36= 27`

Similarly to get the minimum area, side 8 of `Delta A` will correspond to side 6 of `Delta B`.
Sides are in the ratio `6 : 8` and areas `36 : 64`

Minimum area of `Delta B = (27*36)/64= 15.1875`