Question

Triangle A has an area of `6` and two sides of lengths `8` and `12`. 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 area 7.5938 and Minimum area 3.375

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 8 of `Delta A`.

Sides are in the ratio 9 : 8
Hence the areas will be in the ratio of `9^2 : 8^2 = 81 : 64`

Maximum Area of triangle `B =( 6 * 81) / 64= 7.5938`

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 = (6*81)/144= 3.375`