Triangle A has an area of 5 and two sides of lengths 9 and 12 . Triangle B is similar to triangle A and has a side with a length of 25 . What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 7, 2017

Maximum area 38.5802 and Minimum area 21.7014

Explanation:

Delta s A and B are similar.

To get the maximum area of Delta B, side 25 of Delta B should correspond to side 9 of Delta A.

Sides are in the ratio 25 : 9
Hence the areas will be in the ratio of 25^2 : 9^2 = 625 : 81

Maximum Area of triangle B =( 5 * 625) / 81= 38.5802

Similarly to get the minimum area, side 12 of Delta A will correspond to side 25 of Delta B.
Sides are in the ratio 25 : 12 and areas 625 : 144

Minimum area of Delta B = (5*625)/144= 21.7014