Question

Triangle A has an area of `18` and two sides of lengths `8` and `7`. Triangle B is similar to triangle A and has a side of length `5`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 9.1837
Minimum possible area of triangle B = 7.0313

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 5 of `Delta B` should correspond to side 7 of `Delta A`.

Sides are in the ratio 5 : 17
Hence the areas will be in the ratio of `5^2 : 7^2 = 25 : 49`

Maximum Area of triangle `B =( 18 * 25) / 49= 9.1837`

Similarly to get the minimum area, side 8 of `Delta A` will correspond to side 5 of `Delta B`.
Sides are in the ratio `5 : 8` and areas `25 : 64`

Minimum area of `Delta B = (18*25)/64= 7.0313`