Triangle A has an area of #5 # and two sides of lengths #9 # and #3 #. 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 347.2222 and Minimum area 38.5802

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 3 of #Delta A#.

Sides are in the ratio 25 : 3
Hence the areas will be in the ratio of #25^2 : 3^2 = 625 : 9#

Maximum Area of triangle #B =( 5 * 625) / 9= 347.2222#

Similarly to get the minimum area, side 9 of #Delta A # will correspond to side 25 of #Delta B#.
Sides are in the ratio # 25 : 9# and areas #625 : 81#

Minimum area of #Delta B = (5*625)/81= 38.5802#