Question

Triangle A has an area of `3` and two sides of lengths `6` and `7`. Triangle B is similar to triangle A and has a side of length `15`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area `18.75` and Minimum area `13.7755`

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 6 of `Delta A`.

Sides are in the ratio 15 : 6
Hence the areas will be in the ratio of `15^2 : 6^2 = 225 : 36`

Maximum Area of triangle `B =( 3 * 225) / 36 = 18.75`

Similarly to get the minimum area, side 7 of `Delta A` will correspond to side 15 of `Delta B`.
Sides are in the ratio `15 : 7` and areas `225 : 49`

Minimum area of `Delta B = (3*225)/49= 13.7755`