Question

Triangle A has an area of `4` and two sides of lengths `8` and `7`. Triangle B is similar to triangle A and has a side with a length of `13`. What are the maximum and minimum possible areas of triangle B?

Answer 1

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 13 of `Delta B` should correspond to side 7 of `Delta A`.

Sides are in the ratio 13 : 7
Hence the areas will be in the ratio of `13^2 : 7^2 = 625 : 49`

Maximum Area of triangle `B =( 4 * 169) / 49= 13.7959`

Similarly to get the minimum area, side 8 of `Delta A` will correspond to side 13 of `Delta B`.
Sides are in the ratio `13 : 8` and areas `169 : 64`

Minimum area of `Delta B = (4*169)/64= 10.5625`