Answer:
Used wire in circle  x = 2.64 m
Used in square   L - x = 3.36 m
Total wire used 6 m
Step-by-step explanation:
We have a wire of 6 meters long. 
We will cut it a distance x from one end, to get two pieces
x    and   6 - x
We are going to use the piece x  to get the circle then
So Perimetr of a circle is 2π*r    (r is the radius of the circle) then:
x = 2*π*r    ⇒    r = x/2*π
And area would be  A(c) = π* (x/2*π)²   ⇒ A(c) = x²/4π
From 6 - x we will get a square, and as the perimeter is 4 times the side
we have
( 6 - x )/ 4  is the side of the square
And the area is  A(s) = [( 6 - x ) /4]²
Total area as function of x is
A(t)  = A(c) + A(s)
A(x)  =  x²/4π  + [ ( 6  -  x  ) / 4 ]²
A(x)  =   x²/4π  + (36 + x² - 12x) /16
A(x)  = 1 / 16π [ 4x² + 36π + πx² -  12π x ]
Taking drivatives on both sides of the equation we get:
A´(x) = 1/ 16π [8x +2πx - 12π]
A´(x) = 0    ⇒      1/ 16π [8x +2πx - 12π]  = 0
 [8x +2πx - 12π]  = 0
8x + 6.28x -  37.68  = 0
14.28x - 37.68 =  0      ⇒  x  = 37.68 /14.28
x = 2.64 m   length of wire used in the circle
Then the length L  for the side of the square is  
(6 - x )/4    ⇒ ( 6 - 2.64 )/ 4   ⇒ 3.36 / 4    
L = 0.84 m   total length of wire used in the square is 
3.36 m
And total length of wire used is 6 m
The function is a quadratic  function and "a" coefficient is positive then is open upward parabola there is not a maximun