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Let s = the length of the side of the original square.
If you increase this by 8 cm (s+8) and square it ((s+8)*(s+8)) you get 169 sq.cm. So you can write:
Square the left side.
Subtract 169 from both sides.
Factor this quadratic equation.
Apply the zero product rule:
which means that...
Discard the negative solution as the length of the sides can only be positive.
cm This is the length of the side of the original square.