Question

Triangle A has an area of `36` and two sides of lengths `8` and `15`. Triangle B is similar to triangle A and has a side with a length of `15`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 126.5625
Minimum possible area of triangle B = 36

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 15 of `Delta B` should correspond to side 8 of `Delta A`.

Sides are in the ratio 15 : 8
Hence the areas will be in the ratio of `15^2 : 8^2 = 225 : 64`

Maximum Area of triangle `B =( 36 * 225) / 64= 126.5625`

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

Minimum area of `Delta B = (36*225)/225= 36`