Triangle A has an area of #18 # and two sides of lengths #8 # and #12 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
Dec 21, 2017

Maximum possible area of triangle B = 18
Minimum possible area of triangle B = 8

Explanation:

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 8 of #Delta B# should correspond to side 8 of #Delta A#.

Sides are in the ratio 8 : 8
Hence the areas will be in the ratio of #8^2 : 8^2 = 64 : 64#

Maximum Area of triangle #B =( 18 * 64) / 64= 18#

Similarly to get the minimum area, side 12 of #Delta A # will correspond to side 8 of #Delta B#.
Sides are in the ratio # 8 : 12# and areas #64 : 144#

Minimum area of #Delta B = (18*64)/144= 8#