Question

Triangle A has an area of `5` and two sides of lengths `9` and `3`. 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 347.2222 and Minimum area 38.5802

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 3 of `Delta A`.

Sides are in the ratio 25 : 3
Hence the areas will be in the ratio of `25^2 : 3^2 = 625 : 9`

Maximum Area of triangle `B =( 5 * 625) / 9= 347.2222`

Similarly to get the minimum area, side 9 of `Delta A` will correspond to side 25 of `Delta B`.
Sides are in the ratio `25 : 9` and areas `625 : 81`

Minimum area of `Delta B = (5*625)/81= 38.5802`