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?
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 ...
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 ...
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