Question

Triangle A has an area of `27` and two sides of lengths `8` and `12`. 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 60.75 and Minimum area 27

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 8 of `Delta A`.

Sides are in the ratio 12 : 8
Hence the areas will be in the ratio of `12^2 : 8^2 = 144 : 64`

Maximum Area of triangle `B =( 27 * 144) / 64= 60.75`

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

Minimum area of `Delta B = (27*144)/144= 27`