Question

Triangle A has an area of `3` and two sides of lengths `5` 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

Maximum area 36.75 and Minimum area 23.52

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 : 9`

Maximum Area of triangle `B =( 3 * 196) / 16= 36.75`

Similarly to get the minimum area, side 5 of `Delta A` will correspond to side 14 of `Delta B`.
Sides are in the ratio `14 : 5` and areas `196 : 25`

Minimum area of `Delta B = (3*196)/25= 23.52`