Question

Triangle A has an area of `4` and two sides of lengths `9` and `7`. 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 area 83.5918 and Minimum area 50.5679

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 7 of `Delta A`.

Sides are in the ratio 32 : 7
Hence the areas will be in the ratio of `32^2 : 7^2 = 625 : 144`

Maximum Area of triangle `B =( 4 * 1024) / 49= 83.5918`

Similarly to get the minimum area, side 9 of `Delta A` will correspond to side 32 of `Delta B`.
Sides are in the ratio `32 : 9` and areas `1024 : 81`

Minimum area of `Delta B = (4*1024)/81= 50.5679`