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Triangle A has an area of #6 # and two sides of lengths #8 # and #12 #. Triangle B is similar to triangle A and has a side with a length of #9 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

Sadie Allen

Maximum area 7.5938 and Minimum area 3.375

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 9 of #Delta B# should correspond to side 8 of #Delta A#.

Sides are in the ratio 9 : 8 Hence the areas will be in the ratio of #9^2 : 8^2 = 81 : 64#

Maximum Area of triangle #B =( 6 * 81) / 64= 7.5938#

Similarly to get the minimum area, side 12 of #Delta A # will correspond to side 9 of #Delta B#. Sides are in the ratio # 9 : 12# and areas #81 : 144#

Minimum area of #Delta B = (6*81)/144= 3.375#

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