Question

Triangle A has an area of `18` and two sides of lengths `5` 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 of triangle B = 103.68

Minimum area of triangle B = 32

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 5 of `Delta A`.

Sides are in the ratio 12 : 5.
Hence the areas will be in the ratio of `12^2 : 5^2 = 144 : 25`

Maximum Area of triangle `B =( 18 * 144) / 25 = 103.68`

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 = (18*144)/81 = 32`