Question

Triangle A has an area of `9` and two sides of lengths `3` and `8`. Triangle B is similar to triangle A and has a side with a length of `7`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum possible area of triangle B = 49
Minimum possible area of triangle B = 6.8906

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 7 of `Delta B` should correspond to side 3 of `Delta A`.

Sides are in the ratio 7 : 3
Hence the areas will be in the ratio of `7^2 : 3^2 = 49 : 9`

Maximum Area of triangle `B =( 9 * 49) / 9= 49`

Similarly to get the minimum area, side 8 of `Delta A` will correspond to side 7 of `Delta B`.
Sides are in the ratio `7 : 8` and areas `49 : 64`

Minimum area of `Delta B = (9*49)/64= 6.8906`