Question

Triangle A has an area of `60` and two sides of lengths `12` and `15`. 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 area 33.75 and Minimum area 21.6

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 25 of `Delta B` should correspond to side 12 of `Delta A`.

Sides are in the ratio 9 : 12
Hence the areas will be in the ratio of `9^2 : 12^2 = 81 : 144`

Maximum Area of triangle `B =( 60 * 81) / 144= 33.75`

Similarly to get the minimum area, side 15 of `Delta A` will correspond to side 9 of `Delta B`.
Sides are in the ratio `9 : 15` and areas `81 : 225`

Minimum area of `Delta B = (60*81)/225= 21.6`