Question 785390
{{{x}}}= outer side of the concrete walk (in meters)
Since there are {{{red(2)}}} meters of concrete walk to either side of the pool, the length of one side of the pool,
{{{x-2*red(2)=x-4}}}= length of the side of the pool (in meters).
{{{x*x=x^2}}}= total area of the pool plus concrete walk (in square meters)
{{{(x-4)^2}}} area of the pool (in square meters).
What the problem says in words translates as 
{{{(x-4)^2=(2/3)*x^2}}}
{{{x^2-8x+16=(2/3)x^2}}}
Multiplying times 3 both sides of the equation, we get
{{{3(x^2-8x+16)=2x^2}}}
{{{3x^2-24x+48=2x^2}}}
{{{3x^2-24x+48-2x^2=0}}
{{{x^2-24x+48=0}}}
Solving that quadratic equation, we get two solutions.
One is negative, which does not make sense.
The other one is
{{{x=12+4sqrt(6)="approx."}}}{{{21.8}}}
The outside dimensions of the walk are 21.8 meters by 21.8 meters.
(The pool sides measure 21.8 meters - 4 meters = 17.8 meters).
 
SOLVING THE QUADRATIC EQUATION:
Using the quadratic formula:
{{{x = (-(-24) +- sqrt((-24)^2-4*1*48 ))/(2*1) }}}
{{{x = (24 +- sqrt(576-192))/2}}}
{{{x = (24 +- sqrt(384))/2}}}
{{{x = (24 +- sqrt(64*6))/2}}}
{{{x = (24 +- sqrt(64)*sqrt(6))/2}}}
{{{x = (24 +- 8*sqrt(6))/2}}}
{{{x = 12 +- 4*sqrt(6)}}}
Completing the square:
{{{x^2-24x+48=0}}}
{{{x^2-24x=-48}}}
{{{x^2-24x+144=-48+144}}}
{{{(x-12)^2=96}}}
{{{x=12 +- sqrt(96)}}}
{{{x=12 +- sqrt(16*6)}}}
{{{x=12 +- sqrt(16)*sqrt(6)}}}
{{{x=12 +- 4sqrt(6)}}}