do some setup and I'm sure you will find that the problem is solved by a regular n-gon regardless of the number of sides.
Just define the third side in terms of the included angle.
Two sides of a triangle are 4 inches long. What should be the angle between these sides to make the area of the triangle as large as possible?
3 answers
Since you are in Calculus, I assume you know the area of a triangle is (1/2) ab sinØ, where Ø is the contained angle between a and b
A = (1/2)(4)(4)sinØ
A = 8sinØ
dA/dØ = 8cosØ
for a max of A, 8cosØ = 0
Ø = 90° or 270°
but we are in a triangle so the angle must be 90° for the largest area
A = (1/2)(4)(4)sinØ
A = 8sinØ
dA/dØ = 8cosØ
for a max of A, 8cosØ = 0
Ø = 90° or 270°
but we are in a triangle so the angle must be 90° for the largest area
Not what I expected, but quite true. The equilateral triangle has area 4√3 < 8