Triangle A has an area of #60 # and two sides of lengths #12 # 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?
Maximum area 10.4167 and Minimum area 6.6667
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The maximum and minimum possible areas of Triangle B can be calculated based on the ratio of the corresponding sides of Triangle B to Triangle A.
Given that Triangle B is similar to Triangle A, the ratio of corresponding sides is constant.
Let's denote the ratio of corresponding sides of Triangle B to Triangle A as ( k ).
The ratio of corresponding sides of Triangle B to Triangle A is given by: [ k = \frac{5}{15} = \frac{1}{3} ]
Therefore, the ratio ( k ) is ( \frac{1}{3} ).
Now, to find the maximum and minimum possible areas of Triangle B:
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Maximum Area: [ \text{Max Area of B} = (\text{Max Area of A}) \times k^2 ] [ \text{Max Area of B} = (60) \times \left(\frac{1}{3}\right)^2 ] [ \text{Max Area of B} = 60 \times \frac{1}{9} ] [ \text{Max Area of B} = 6.67 ]
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Minimum Area: [ \text{Min Area of B} = (\text{Min Area of A}) \times k^2 ] [ \text{Min Area of B} = (60) \times \left(\frac{1}{3}\right)^2 ] [ \text{Min Area of B} = 60 \times \frac{1}{9} ] [ \text{Min Area of B} = 6.67 ]
Therefore, the maximum possible area of Triangle B is ( 6.67 ) square units and the minimum possible area is also ( 6.67 ) 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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