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 form
Let us assume the length of one side of this square as l.
Therefore the sum of four sides will be l+l+l+l = 4l
Now perimeter of the square = sum of all sides = 4l (from above)
we know in this problem perimeter is 64 in.
Therefore 64 = 4l
Divide each side by 4
16 = l
Hence, 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 16
Length of side of new square = 8in (Answer)