Question

Triangle A has an area of `6` and two sides of lengths `9` and `4`. Triangle B is similar to triangle A and has a side with a length of `14`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Possible maximum area of triangle B = 73.5
Possible minimum area of triangle B = 14.5185

Explanation:

`Delta s A and B` are similar.

To get the maximum area of `Delta B`, side 14 of `Delta B` should correspond to side 4 of `Delta A`.

Sides are in the ratio 14 : 4
Hence the areas will be in the ratio of `14^2 : 4^2 = 196 : 16`

Maximum Area of triangle `B =( 6 * 196) / 16= 73.5`

Similarly to get the minimum area, side 9 of `Delta A` will correspond to side 14 of `Delta B`.
Sides are in the ratio `14 : 9` and areas `196 : 81`

Minimum area of `Delta B = (6*196)/81= 14.5185`