When each side of a given square is increased by 4 feets the area is increased by 64 feet determine the dimensions of original square?

Suppose the length of a side in the original square was S feet, so that the original area was S2 square feet.

The incresed side is (S+4) feet [not feets!] giving a new area of (s+4)2 sq feet.

So (S+4)2 = S2 + 64

S2 + 8x + 16 = S2 + 64

8S = 48

and so S = 6 ft