Question

Triangle A has an area of `8` and two sides of lengths `4` and `7`. 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 128 and Minimum area 41.7959

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 4 of `Delta A`.

Sides are in the ratio 16 : 4
Hence the areas will be in the ratio of `16^2 : 4^2 = 256 : 16`

Maximum Area of triangle `B =( 8 * 256) / 16= 128`

Similarly to get the minimum area, side 7 of `Delta A` will correspond to side 16 of `Delta B`.
Sides are in the ratio `16 : 7` and areas `256 : 49`

Minimum area of `Delta B = (8*256)/49= 41.7959`