Triangle A has an area of #24 # and two sides of lengths #8 # and #12 #. 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?
Using either given side as a base, the third side can be calculated.
NOW we know that the SMALLEST similar triangle "B" must have the largest side as 5, and the LARGEST similar triangle will have the smallest side with a length of 5. The corresponding ratios are:
Using Herron's Rule directly saves some further angle computation.