Question

Triangle A has an area of `12` and two sides of lengths `6` and `9`. Triangle B is similar to triangle A and has a side of length `12`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area 48 and Minimum area 21.3333**

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 12 of `Delta B` should correspond to side 6 of `Delta A`.

Sides are in the ratio 12 : 6
Hence the areas will be in the ratio of `12^2 : 6^2 = 144 : 36`

Maximum Area of triangle `B =( 12 * 144) / 36= 48`

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

Minimum area of `Delta B = (12*144)/81= 21.3333`