Question

Triangle A has an area of `4` and two sides of lengths `4` and `3`. Triangle B is similar to triangle A and has a side with a length of `32`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 455.1111
Minimum possible area of triangle B = 256

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 32 of `Delta B` should correspond to side 3 of `Delta A`.

Sides are in the ratio 32 : 3
Hence the areas will be in the ratio of `32^2 : 3^2 = 1024 : 9`

Maximum Area of triangle `B =( 4 * 1024) / 9= 455.1111`

Similarly to get the minimum area, side 4 of `Delta A` will correspond to side 32 of `Delta B`.
Sides are in the ratio `32 : 4` and areas `1024 : 16`

Minimum area of `Delta B = (4*1024)/16= 256`