Question

Triangle A has an area of `9` and two sides of lengths `8` and `4`. Triangle B is similar to triangle A and has a side with a length of `8`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area 36 and Minimum area 9

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 8 of `Delta B` should correspond to side 4 of `Delta A`.

Sides are in the ratio 8 : 4
Hence the areas will be in the ratio of `8^2 : 4^2 = 64 : 16`

Maximum Area of triangle `B =( 9 * 64) / 16= 36`

Similarly to get the minimum area, side 8 of `Delta A` will correspond to side 8 of `Delta B`.
Sides are in the ratio `6 : 8` and areas `64 : 64`

Minimum area of `Delta B = (9*64)/64= 9`