Question

Triangle A has an area of `32` and two sides of lengths `8` and `9`. 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 area 112.5 and Minimum area 88.8889

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 =( 32 * 225) / 64= 112.5`

Similarly to get the minimum area, side 9 of `Delta A` will correspond to side 15 of `Delta B`.
Sides are in the ratio `15 : 9` and areas `225 : 81`

Minimum area of `Delta B = (32*225)/81= 88.8889`