Answer:
Length of wire for circle is 0.44 ft
Length of wire for square is 0.56 ft
Step-by-step explanation:
Let x is circumference of the circle
then
(1-x) = perimeter of the square
Find the radius of the circle
r = (x/2.π)
Find the area of the circle
a = π(x/2π)^2
a = π(x^2/4π^2)
Cancel π
a = x^2/4π
Find the area of the square:
a = (1-x/4)^2
a = (1-2x+x^2)/16
Total area
A = (x^2/4π)+(1-2x+x^2/16)
A = 4x^2+3.142-6.284x+3.142x^2
A = 7.142x^2-6.284x+3.142
Find the axis of symmetry [x = -b/(2a)]
x = -(-6.284)/{2.(7.142)}
x = 6.284/14.284
x = 0.44 ft, the piece of wire creating a circle
and
1 - 0.44 = 0.56 ft, the piece of wire creating the square
These lengths should give minimum area of the circle and square together
