# Triangle A has an area of #4 # and two sides of lengths #8 # and #4 #. Triangle B is similar to triangle A and has a side with a length of #13 #. What are the maximum and minimum possible areas of triangle B?

Using Heron's Formula,

we have

Thus,

Complete the square.

This shows that there are 2 possible kinds of triangle that satisfy the conditions given.

Therefore, the linear scale ratio is

The area is therefore enlarged to a factor that is the square of the linear scale ratio. Therefore, The max area triangle B can have is

Therefore, the linear scale ratio is

The area is therefore enlarged to a factor that is the square of the linear scale ratio. Therefore, The min area triangle B can have is

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