Triangle A has an area of #5 # and two sides of lengths #6 # and #7 #. Triangle B is similar to triangle A and has a side of length #15 #. What are the maximum and minimum possible areas of triangle B?
Maximum area of
Minimum area of
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To find the maximum and minimum possible areas of triangle B, we need to consider the properties of similar triangles.
Since triangle B is similar to triangle A, the ratios of corresponding sides are equal. Therefore, the ratio of the side lengths of triangle B to those of triangle A is 15/6 = 5/2.
To find the maximum possible area of triangle B, we maximize the ratio of the areas of the two triangles. Since the ratio of the areas of similar figures is equal to the square of the ratio of their corresponding sides, the maximum area of triangle B occurs when the ratio of the areas of the two triangles is the square of 5/2, which is (5/2)^2 = 25/4. Therefore, the maximum area of triangle B is 25 times the area of triangle A, or 5 * 25/4 = 31.25.
To find the minimum possible area of triangle B, we minimize the ratio of the areas of the two triangles. The minimum area of triangle B occurs when the ratio of the areas of the two triangles is the square of the reciprocal of 5/2, which is (2/5)^2 = 4/25. Therefore, the minimum area of triangle B is 4 times the area of triangle A, or 5 * 4/25 = 0.8.
So, the maximum possible area of triangle B is 31.25 square units, and the minimum possible area is 0.8 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.
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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