Question

Triangle A has an area of `18` and two sides of lengths `9` and `14`. Triangle B is similar to triangle A and has a side of length `8`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area 14.2222 and Minimum area 5.8776

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 9 of `Delta A`.

Sides are in the ratio 8 : 9
Hence the areas will be in the ratio of `8^2 : 9^2 = 64 : 81`

Maximum Area of triangle `B =( 18 * 64) / 81= 14.2222`

Similarly to get the minimum area, side 14 of `Delta A` will correspond to side 8 of `Delta B`.
Sides are in the ratio `8 : 14` and areas `64 : 196`

Minimum area of `Delta B = (18*64)/196= 5.8776`