Question

Triangle A has an area of `32` and two sides of lengths `12` and `15`. Triangle B is similar to triangle A and has a side with a length of `25`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 138.8889
Minimum possible area of triangle B = 88.8889

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 12 of `Delta A`.

Sides are in the ratio 25 : 12
Hence the areas will be in the ratio of `25^2 : 12^2 = 625 : 144`

Maximum Area of triangle `B =( 32 * 625) / 144= 138.8889`

Similarly to get the minimum area, side 15 of `Delta A` will correspond to side 25 of `Delta B`.
Sides are in the ratio `25 : 15` and areas `625 : 225`

Minimum area of `Delta B = (32*625)/225= 88.8889`