Triangle A has an area of #12 # and two sides of lengths #3 # and #8 #. 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 = 108
Minimum possible area of triangle B = 15.1875

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 3 of #Delta A#.

Sides are in the ratio 9 : 3
Hence the areas will be in the ratio of #9^2 : 3^2 = 81 : 9#

Maximum Area of triangle #B =( 12 * 81) / 9= 108#

Similarly to get the minimum area, side 8 of #Delta A # will correspond to side 9 of #Delta B#.
Sides are in the ratio # 9 : 8# and areas #81 : 64#

Minimum area of #Delta B = (12*81)/64= 15.1875#