Triangle A has an area of #32 # and two sides of lengths #12 # and #15 #. Triangle B is similar to triangle A and has a side with a length of #25 #. What are the maximum and minimum possible areas of triangle B?
Maximum possible area of triangle B = 138.8889
Minimum possible area of triangle B = 88.8889
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Since Triangle B is similar to Triangle A, their corresponding sides are proportional. Let's denote the area of Triangle B as ( A_B ).
The ratio of corresponding sides of similar triangles is the same. Therefore, if the side lengths of Triangle B are in the ratio ( \frac{25}{12} ) or ( \frac{25}{15} ) to the corresponding sides of Triangle A, then the area of Triangle B would be in the square of those ratios compared to Triangle A.
Let's calculate the areas using these ratios:

For the ratio ( \frac{25}{12} ): [ A_B = \left( \frac{25}{12} \right)^2 \times 32 ]

For the ratio ( \frac{25}{15} ): [ A_B = \left( \frac{25}{15} \right)^2 \times 32 ]
Calculating these values will give us the maximum and minimum possible areas of Triangle B.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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