Question

Triangle A has an area of `9` and two sides of lengths `4` and `6`. Triangle B is similar to triangle A and has a side with a length of `16`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 144
Minimum possible area of triangle B = 64

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 25 of `Delta B` should correspond to side 4 of `Delta A`.

Sides are in the ratio 16 : 4
Hence the areas will be in the ratio of `16^2 : 4^2 = 256 : 16`

Maximum Area of triangle `B =( 9 * 256) / 16= 144`

Similarly to get the minimum area, side 6 of `Delta A` will correspond to side 16 of `Delta B`.
Sides are in the ratio `16 : 6` and areas `256 : 36`

Minimum area of `Delta B = (9*256)/36= 64`