Given information: 1) Object in question is a square. By definition we know square has all the four sides of same length. 2) We know the perimeter of the square is 64 in . Again a perimeter of an object is the sum of all its sides. Now, let us plug this information in some kind of mathematical formLet us assume the length of one side of this square as l. Therefore the sum of four sides will be l+l+l+l = 4lNow perimeter of the square = sum of all sides = 4l (from above)we know in this problem perimeter is 64 in. Therefore 64 = 4lDivide each side by 416 = lHence, the length of the original square is 16 inch. Now the length of the new square is 1/2 of the length of the original square. Length of side of new square = 1/2 X length of side of original square. Length of side of new square = 1/2 X 16Length of side of new square = 8in (Answer)