Question

Triangle A has an area of `24` and two sides of lengths `12` and `6`. 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 = 54
Minimum possible area of triangle B = 13.5

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 6 of `Delta A`.

Sides are in the ratio 9 : 6
Hence the areas will be in the ratio of `9^2 : 6^2 = 81 : 36`

Maximum Area of triangle `B =( 24 * 81) / 36= 54`

Similarly to get the minimum area, side 12 of `Delta A` will correspond to side 9 of `Delta B`.
Sides are in the ratio `9 : 12` and areas `81 : 144`

Minimum area of `Delta B = (24*81)/144= 13.5`