Question

Triangle A has an area of `8` and two sides of lengths `6` and `3`. Triangle B is similar to triangle A and has a side with a length of `16`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area `227.5556` and Minimum area `56.8889`

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 16 of `Delta B` should correspond to side 3 of `Delta A`.

Sides are in the ratio 16 : 3
Hence the areas will be in the ratio of `16^2 : 3^2 = 256 : 9`

Maximum Area of triangle `B =( 8 * 256) / 9= 227.5556`

Similarly to get the minimum area, side 6 of `Delta A` will correspond to side 16 of `Delta B`.
Sides are in the ratio `16 : 6` and areas `256 : 36`

Minimum area of `Delta B = (8*256)/36= 56.8889`