In this post, I will deal with an interesting high school math problem. Suppose we are given the following triangle:
We have two parameters:
- , the number of circles touching a side of the triangle,
- , the radius of each circle.
In order to find out the area of the triangle given the parameters , , we need to find the length of each side. Basically, we must calculate in Figure 2 as a function of , which is fairly easy since we must have
Next, we can define the length of a side of the triangle as a function of and :
If we set (i.e., is the half of the perimeter of the triangle),
by Heron’s formula, we have that the area of the triangle is