Question

Triangle A has an area of `15` and two sides of lengths `8` 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 area of `Delta B = 78.3673`
Minimum area of `Delta B = 48`

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 7 of `Delta A`.

Sides are in the ratio 16 : 7
Hence the areas will be in the ratio of `16^2 : 7^2 = 256 : 49`

Maximum Area of triangle `B =( 15 * 256) / 49= 78.3673`

Similarly to get the minimum area, side 8 of `Delta A` will correspond to side 16 of `Delta B`.
Sides are in the ratio `16 : 8` and areas `256 : 64`

Minimum area of `Delta B = (12*256)/64= 48`