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Triangle A has an area of #11 # and two sides of lengths #4 # and #6 #. 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

Evelyn Arboleda

Maximum possible area of triangle B = 176
Minimum possible area of triangle B = 78.2222

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 16 of #Delta B# should correspond to side 4 of #Delta A#.

Sides are in the ratio 16 : 4 Hence the areas will be in the ratio of #16^2 : 4^2 = 256 : 16#

Maximum Area of triangle #B =( 11 * 256) / 16= 176#

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 = (11*256)/36= 78.2222#

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Answer 2

Claire Akin

The maximum possible area of triangle B is 176 and the minimum possible area is 44.

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Answer from HIX Tutor

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