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 `9`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 24.7959
Minimum possible area of triangle B = 18.9844

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 9 of `Delta B` should correspond to side 7 of `Delta A`.

Sides are in the ratio 9 : 7
Hence the areas will be in the ratio of `9^2 : 7^2 = 81 : 49`

Maximum Area of triangle `B =( 15 * 81) / 49= 24.7959`

Similarly to get the minimum area, side 15 of `Delta A` will correspond to side 9 of `Delta B`.
Sides are in the ratio `9 : 8` and areas `81 : 64`

Minimum area of `Delta B = (15*81)/64= 18.9844`