Triangle A has an area of #6 # and two sides of lengths #9 # and #4 #. Triangle B is similar to triangle A and has a side with a length of #14 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 21, 2017

Possible maximum area of triangle B = 73.5
Possible minimum area of triangle B = 14.5185

Explanation:

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 14 of #Delta B# should correspond to side 4 of #Delta A#.

Sides are in the ratio 14 : 4
Hence the areas will be in the ratio of #14^2 : 4^2 = 196 : 16#

Maximum Area of triangle #B =( 6 * 196) / 16= 73.5#

Similarly to get the minimum area, side 9 of #Delta A # will correspond to side 14 of #Delta B#.
Sides are in the ratio # 14 : 9# and areas #196 : 81#

Minimum area of #Delta B = (6*196)/81= 14.5185#