Triangle A has an area of #24 # and two sides of lengths #12 # and #6 #. Triangle B is similar to triangle A and has a side of length #9 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 21, 2017

Maximum possible area of triangle B = 54
Minimum possible area of triangle B = 13.5

Explanation:

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 9 of #Delta B# should correspond to side 6 of #Delta A#.

Sides are in the ratio 9 : 6
Hence the areas will be in the ratio of #9^2 : 6^2 = 81 : 36#

Maximum Area of triangle #B =( 24 * 81) / 36= 54#

Similarly to get the minimum area, side 12 of #Delta A # will correspond to side 9 of #Delta B#.
Sides are in the ratio # 9 : 12# and areas #81 : 144#

Minimum area of #Delta B = (24*81)/144= 13.5#