Triangle A has an area of 8 8 and two sides of lengths 6 6 and 3 3. Triangle B is similar to triangle A and has a side with a length of 16 16. What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 7, 2017

Maximum area 227.5556227.5556 and Minimum area 56.888956.8889

Explanation:

Delta s A and B ΔsAandB are similar.

To get the maximum area of Delta B, side 16 of Delta B should correspond to side 3 of Delta A.

Sides are in the ratio 16 : 3
Hence the areas will be in the ratio of 16^2 : 3^2 = 256 : 9

Maximum Area of triangle B =( 8 * 256) / 9= 227.5556

Similarly to get the minimum area, side 6 of Delta A will correspond to side 16 of Delta B.
Sides are in the ratio 16 : 6 and areas 256 : 36

Minimum area of Delta B = (8*256)/36= 56.8889