Triangle A has an area of #8 # and two sides of lengths #4 # and #7 #. 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

Maximum 128 and Minimum area 41.7959

#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 =( 8 * 256) / 16= 128#

Similarly to get the minimum area, side 7 of #Delta A # will correspond to side 16 of #Delta B#. Sides are in the ratio # 16 : 7# and areas #256 : 49#

Minimum area of #Delta B = (8*256)/49= 41.7959#

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Answer 2

Sophia Alfred

The maximum possible area of triangle B is $128$ square units, and the minimum possible area is $32$ square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.