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Triangle A has an area of #8 # and two sides of lengths #6 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

Autumn Armstrong

Maximum area #227.5556# and Minimum area #56.8889#

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 16 of #Delta B# should correspond to side 3 of #Delta A#.

Sides are in the ratio 16 : 3 Hence the areas will be in the ratio of #16^2 : 3^2 = 256 : 9#

Maximum Area of triangle #B =( 8 * 256) / 9= 227.5556#

Similarly to get the minimum area, side 6 of #Delta A # will correspond to side 16 of #Delta B#. Sides are in the ratio # 16 : 6# and areas #256 : 36#

Minimum area of #Delta B = (8*256)/36= 56.8889#

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