Triangle A has an area of #27 # and two sides of lengths #12 # and #15 #. 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
Oct 24, 2017

Maximum area of triangle B = 108.5069

Minimum area of triangle B = 69.4444

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 12 of #Delta A#.

Sides are in the ratio 25 : 12
Hence the areas will be in the ratio of #25^2 : 12^2 = 625 : 144#

Maximum Area of triangle #B =( 25 * 625) / 144= 108.5069#

Similarly to get the minimum area, side 15 of #Delta A # will correspond to side 25 of #Delta B#.
Sides are in the ratio # 25 : 15# and areas #625 : 225#

Minimum area of #Delta B = (25*625)/225= 69.4444#