# Triangle A has an area of #24 # and two sides of lengths #8 # and #15 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the maximum and minimum possible areas of triangle B?

Case 1.

Case 2.

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The maximum possible area of triangle B occurs when its side of length 5 is proportional to the longest side of triangle A, which is 15. Therefore, the maximum area of triangle B can be found using the ratio of the squares of corresponding sides:

Maximum area of triangle B = (5/15)^2 * Area of triangle A = (1/9) * 24 = 8/3 square units

The minimum possible area of triangle B occurs when its side of length 5 is proportional to the shortest side of triangle A, which is 8. Therefore, the minimum area of triangle B can be found using the ratio of the squares of corresponding sides:

Minimum area of triangle B = (5/8)^2 * Area of triangle A = (25/64) * 24 = 9.375 square units

So, the maximum possible area of triangle B is 8/3 square units, and the minimum possible area is 9.375 square units.

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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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