Question 184171
Let S be the length of the side of the original square.
The area of the original square is expressed by {{{A[o] = S^2}}}
When the side, S, is increased by 8cm, the length of the side of the new square becomes S+8 and the new area is expressed as: {{{A[n] = (S+8)^2}}} and this is equal to 144 sq.cm.
So you can set up the equation to solve for S...
{{{(S+8)^2 = 144}}} 
{{{S^2+16S+64 = 144}}} Subtract 144 from both sides.
{{{highlight(S^2+16S-80 = 0)}}} Factor this quadratic equation.
{{{S-4)(S+20) = 0}}} Apply the zero product rule:
{{{S-4 = 0}}} or {{{S+20 = 0}}} so...
{{{highlight(S = 4)}}} or {{{S = -20}}} Discard the negative solution as the length must be a positive value.
The length of the side of the original square is 4cm.