Triangle A has an area of #27 # and two sides of lengths #8 # and #6 #. Triangle B is similar to triangle A and has a side with a length of #6 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 18, 2017

Maximum area of #Delt B = 27#
Minimum area of #Delta B = 15.1875#

Explanation:

#Delta s A and B # are similar.

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

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

Maximum Area of triangle #B =( 27 * 36) / 36= 27#

Similarly to get the minimum area, side 8 of #Delta A # will correspond to side 6 of #Delta B#.
Sides are in the ratio # 6 : 8# and areas #36 : 64#

Minimum area of #Delta B = (27*36)/64= 15.1875#