Triangle A has an area of #18 # and two sides of lengths #5 # and #9 #. Triangle B is similar to triangle A and has a side of length #12 #. What are the maximum and minimum possible areas of triangle B?
- Maximum possible are = 103.8
- Minimum possible area = 16.2
(but see note below)
We are given that in the triangle
Since the area of the triangle is 18 (see below), we know that the length of the altitude
Now, we can have either of the two situations depicted in the figure below
In either case, In Case A : In Case B : Hence the side Since For the second triangle, the area will be the largest (resp. smallest) if the given side (of length 12)is its smallest (resp. largest) side. Thus, the smallest possible area is the smallest possible area is Note
which would yield a quadratic for
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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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