Question

Triangle A has an area of `5` and two sides of lengths `9` and `12`. 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 area 38.5802 and Minimum area 21.7014

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 9 of `Delta A`.

Sides are in the ratio 25 : 9
Hence the areas will be in the ratio of `25^2 : 9^2 = 625 : 81`

Maximum Area of triangle `B =( 5 * 625) / 81= 38.5802`

Similarly to get the minimum area, side 12 of `Delta A` will correspond to side 25 of `Delta B`.
Sides are in the ratio `25 : 12` and areas `625 : 144`

Minimum area of `Delta B = (5*625)/144= 21.7014`