Question 192753
Assuming the width of the patio around the pool to be uniform, let's call this x.
The total area of the pool plus patio can be expressed as:
{{{A[t] = (40+2x)(60+2x)}}} and this is twice the area of the pool alone {{{A[p]}}} which means: {{{2*A[p] = 2(60)(40)}}} = {{{2*2400 = 4800}}}, so...
{{{(40+2x)(60+2x) = 4800}}} Multiply and rearrange into standard form:
{{{4x^2+200x+2400 = 4800}}} Divide through by 4 to simplify a bit.
{{{x^2+50x+600 = 1200}}} Subtract 1200 from both sides.
{{{x^2+50x-600 = 0}}} Factor this quadratic equation.
{{{(x-10)(x+60) = 0}}} Apply the zero product rule.
{{{x-10 = 0}}} or {{{x+60 = 0}}} so...
{{{x = 10}}} or {{{x = -60}}} Discard the negative solution 'cause widths are positive quantities.
{{{highlight(x = 10)}}} 
The patio is 10 feet wide.