Triangle A has an area of #4 # and two sides of lengths #4 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #32 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 21, 2017

Maximum possible area of triangle B = 455.1111
Minimum possible area of triangle B = 256

Explanation:

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 32 of #Delta B# should correspond to side 3 of #Delta A#.

Sides are in the ratio 32 : 3
Hence the areas will be in the ratio of #32^2 : 3^2 = 1024 : 9#

Maximum Area of triangle #B =( 4 * 1024) / 9= 455.1111#

Similarly to get the minimum area, side 4 of #Delta A # will correspond to side 32 of #Delta B#.
Sides are in the ratio # 32 : 4# and areas #1024 : 16#

Minimum area of #Delta B = (4*1024)/16= 256#