36 inch wire is cut to 2 pieces every piece is of 18 inch then one shape is square 18/4 is one side of square which is 4.5 inch then area of square= (4.5)^2 = 20.25

now for the other half shape is rectangle where length L is twice the width w so

L=2w

Area of rectangle = area of square according to our condition

Area of rectangle= W*L

Area of rectangle= W*2W

20.25=2W^2

10.125= W^2

W= sqrt(10.125)

W=3.18 inch

this is the width of rectangle that will minimize the area