Answer:
The circumference of the circle is 29.36 cm
Step-by-step explanation:
Let
x -----> the length of first piece (shape of square)
y ------> the length of the other piece (shape of a circle)
we know that
-----> equation A
step 1
<em>Find out the area of square</em>
The perimeter of square is equal to the length of the first piece
where
b is the length side of square
Find the total area A
The area of square is
step 2
<em>Find out the area of the circle</em>
The circumference of the circle is equal to the length of the other piece
The circumference is equal to
so
Find the radius of the circle
Find the area of the circle
substitute the value of r
step 3
Find out the total area
substitute
This is a vertical parabola open upward
The vertex is a minimum
using a graphing tool
The vertex is the point (14.64, 67.77)
see the attached figure
For x=14.64 cm -----> the area is a minimum
The lengths of the wire are
therefore
The circumference of the circle is 29.36 cm