Question

Triangle A has an area of `12` and two sides of lengths `3` and `8`. Triangle B is similar to triangle A and has a side of length `9`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 108
Minimum possible area of triangle B = 15.1875

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 3 of `Delta A`.

Sides are in the ratio 9 : 3
Hence the areas will be in the ratio of `9^2 : 3^2 = 81 : 9`

Maximum Area of triangle `B =( 12 * 81) / 9= 108`

Similarly to get the minimum area, side 8 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 = (12*81)/64= 15.1875`