Triangle A has an area of #4 # and two sides of lengths #9 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #32 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area 83.5918 and Minimum area 50.5679

#Delta s A and B # are similar.
To get the maximum area of #Delta B#, side 32 of #Delta B# should correspond to side 7 of #Delta A#.
Sides are in the ratio 32 : 7 Hence the areas will be in the ratio of #32^2 : 7^2 = 625 : 144#
Maximum Area of triangle #B =( 4 * 1024) / 49= 83.5918#
Similarly to get the minimum area, side 9 of #Delta A # will correspond to side 32 of #Delta B#. Sides are in the ratio # 32 : 9# and areas #1024 : 81#
Minimum area of #Delta B = (4*1024)/81= 50.5679#
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Answer 2

The maximum possible area of Triangle B occurs when its side length is maximized to be equal to the longest side of Triangle A, which is 9. Therefore, the maximum possible area of Triangle B is (4 \times \left(\frac{32}{9}\right)^2 = \frac{4096}{81}).

The minimum possible area of Triangle B occurs when its side length is minimized to be equal to the shortest side of Triangle A, which is 7. Therefore, the minimum possible area of Triangle B is (4 \times \left(\frac{32}{7}\right)^2 = \frac{4096}{49}).

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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.

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.

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.

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.

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