The length of the wire used for making the square is approximately 14.71 meters
Let the length of the wire used for making the square be x meters. Then, the length of the wire used for making the circle is (28 - x) meters.
Let the side of the square be s-meter. Then, the perimeter of the square is 4s = x.
Solving for s, we get s = x/4.
The area of the square is s^2 = (x/4)^2 = x^2/16.
Let the radius of the circle be r meters. Then, the circumference of the circle is 2πr = (28 - x)
Solving for r, we get r = (14 - x/2π).
The area of the circle is πr^2 = π((14 - x/2π)^2)
To minimize the combined area of the square and the circle, we need to minimize the expression:
A(x) = x^2/16 + π((14 - x/2π)^2)
Expanding and simplifying the expression, we get:
A(x) = x^2/16 + 196π - 28πx + x^2/4π
To find the minimum value of A(x), we can take the derivative of A(x) concerning x and set it equal to zero:
dA(x)/dx = x/8 - 14π + x/4π = 0
Solving for x, we get x ≈ 14.71.
Therefore, the length of the wire used for making the square is approximately 14.71 meters, and the length of the wire used for making the circle is approximately 13.29 meters.