# Triangle A has an area of #15 # and two sides of lengths #4 # and #9 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the maximum and minimum possible areas of triangle B?

##### 1 Answer

There's a possible third side of around

If the side length

#### Explanation:

This is perhaps a trickier problem than it first appears. Anybody know how to find the third side, which we seem to need for this problem? Normal trig usual makes us calculate the angles, making an approximation where none is required.

It's not really taught in school, but the easiest way is Archimedes' Theorem, a modern form of Heron's Theorem. Let's call A's area

We have

That's two different values for

For maximal area, maximal scaling, that means the smallest side scales to

For minimal area the largest side scales to