**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