text: Let the wire be cut into lengths x and L-x\nL-x is used to form the square.\nLet each side of the square be s.\nSo 4s = L-x.\ns = (L-x)/4\nArea of square = ((L-x)/4)^2 = (L^2-2Lx+x^2)/16\n\nx is used to form circle\nLet the radius of circle be r.\n2(pi)r = x (circumference of circle)\nr = x/((2)(pi))\nArea of circle = (pi)r^2 = x^2/((4)(pi))\n\nNow to find the minimum area, you need to differentiate\narea of square+area of circle and equate it to zero\nso\nd/dx((area of square)+(area of circle)) = 0\n=>L^2/16-L/8+x/8 +x/((2)(pi))= 0\n=>(pi)L^2- 2(pi)L + (pi+4)x = 0\n\nsolving the equation using the formula for factorization of quadratic equations.. you will get the value for x in terms of L.