Question 4707
The original area of the square is:
  A = s^2  After increasing the sides by 10 cm, the new area is:
9A = (s+10)^2
9A = s^2 + 20s + 100  Substitute the A = s^2
9s^2 = s^2 + 20 s + 100
8s^2 - 20s - 100 = 0  Divide through by 4 then Solve by factoring.
2s^2 - 5s - 25 = 0   Factor.
(2s + 5)(s - 5) = 0  Apply the zero products principle.
2s + 5 = 0;  2s = -5  Discard this as negative lengths are not meaningful.
s - 5 = 0; s = 5

Original length of the sides of the square = 5 cm.

Check:

Original area: A = s^2 = 5^2 = 25 cm^2
New area = 9(25) = 225 cm^2;
  (5 + 10)^2 = 15^2 = 225 cm^2