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Triangle A has an area of #12 # and two sides of lengths #3 # and #8 #. Triangle B is similar to triangle A and has a side of length #9 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

Noah Atkinson

Maximum possible area of triangle B = 108
Minimum possible area of triangle B = 15.1875

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 9 of #Delta B# should correspond to side 3 of #Delta A#.

Sides are in the ratio 9 : 3 Hence the areas will be in the ratio of #9^2 : 3^2 = 81 : 9#

Maximum Area of triangle #B =( 12 * 81) / 9= 108#

Similarly to get the minimum area, side 8 of #Delta A # will correspond to side 9 of #Delta B#. Sides are in the ratio # 9 : 8# and areas #81 : 64#

Minimum area of #Delta B = (12*81)/64= 15.1875#

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Answer 2

Theodore Abad

The maximum possible area of Triangle B is ( 108 ) and the minimum possible area is ( 27 ).

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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.