# Triangle A has an area of #6 # and two sides of lengths #4 # and #6 #. Triangle B is similar to triangle A and has a side of length #18 #. What are the maximum and minimum possible areas of triangle B?

In Triangle A

p = 4, q = 6. Therefore

i.e. r can have values between 2.1 and 9.9, rounded up to one decimal.

Given triangles A & B are similar

Area of triangle

Let side 18 of B proportional to least side 2.1 of A

Then

Let side 18 of B proportional to least side 9.9 of A

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The maximum possible area of triangle B is 108 square units, and the minimum possible area is 24 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.

- Triangle A has sides of lengths #12 #, #16 #, and #8 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the possible lengths of the other two sides of triangle B?
- A triangle has corners at points A, B, and C. Side AB has a length of #45 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #36 #, what is the length of side BC?
- Triangle A has sides of lengths #18 #, #12 #, and #21 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?
- A triangle has corners at points A, B, and C. Side AB has a length of #10 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #8 #, what is the length of side BC?
- Triangle A has an area of #12 # and two sides of lengths #6 # and #9 #. 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?

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