Triangle A has an area of #9 # and two sides of lengths #4 # and #6 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 21, 2017

Maximum possible area of triangle B = 144
Minimum possible area of triangle B = 64

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 4 of #Delta A#.

Sides are in the ratio 16 : 4
Hence the areas will be in the ratio of #16^2 : 4^2 = 256 : 16#

Maximum Area of triangle #B =( 9 * 256) / 16= 144#

Similarly to get the minimum area, side 6 of #Delta A # will correspond to side 16 of #Delta B#.
Sides are in the ratio # 16 : 6# and areas #256 : 36#

Minimum area of #Delta B = (9*256)/36= 64#