Triangle A has an area of #3 # and two sides of lengths #3 # and #6 #. Triangle B is similar to triangle A and has a side with a length of #11 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

The triangle inequality states that the sum of any two sides of a triangle MUST be greater than the 3rd side. That implies the missing side of triangle A must be greater than 3!

Using the triangle inequality ...

#x+3>6# #x>3#

So, the missing side of triangle A must fall between 3 and 6.

This means 3 is the shortest side and 6 is the longest side of triangle A.

Since area is proportional to the square of the ratio of the similar sides ...

minimum area #= (11/6)^2xx3=121/12~~10.1#

maximum area #=(11/3)^2xx3=121/3~~40.3#

Hope that helped

P.S. - If you really want to know the length of the missing 3rd side of triangle A, you can use Heron's area formula and determine that the length is #~~3.325#. I'll leave that proof to you :)

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Answer 2

James Atkins

The maximum possible area of triangle B is (33) and the minimum possible area is (\frac{3}{4}).

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Answer from HIX Tutor

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.