Question

Triangle A has an area of `3` and two sides of lengths `3` and `4`. Triangle B is similar to triangle A and has a side with a length of `11`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area 40.3333# and Minimum area 22.6875**

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 11 of `Delta B` should correspond to side 3 of `Delta A`.

Sides are in the ratio 11 : 3
Hence the areas will be in the ratio of `11^2 : 3^2 = 121 : 9`

Maximum Area of triangle `B =( 3 * 121) / 9 = 40.3333`

Similarly to get the minimum area, side 4 of `Delta A` will correspond to side 11 of `Delta B`.
Sides are in the ratio `11 : 4` and areas `121 : 16`

Minimum area of `Delta B = (3*121)/16= 22.6875`