Answer:
The radius of the circle is
The length of the square is
Step-by-step explanation:
we know that
The circumference of a circle is equal to
The perimeter of the square is equal to
so
Simplify
-----> equation A
The area of a circle is equal to
The area of a square is
The total area is equal to
-----> equation B
substitute equation A in equation B
This is a vertical parabola open upward
The vertex is the minimum
The x-coordinate of the vertex is the radius of the circle that produce a minimum area
The y-coordinate of the vertex is the minimum area
Solve by graphing
The vertex is the point (1.68, 20.164)
see the attached figure
therefore
The radius of the circle is
Find the value of x
assume
