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