Question 164989
Call the width of the pool 
{{{x}}}
The length of the pool will then be 
{{{3x}}}
The area of the pool is 
{{{x*3x = 3x^2}}}
If the deck around the pool is 2.5 m wide, then
{{{2*2.5 = 5}}}m are added to the width of the pool and
{{{2*2.5 = 5}}}m are added to the length of the pool
The area of the pool + deck = 
{{{(x + 5)*(3x + 5) = 3x^2 + 20x + 25}}}
Since it is given that the area of the deck is
{{{A[d] = 265}}}m, The area of the pool is
{{{A[p] = 3x^2 + 20x + 25 - 265}}}, but {{{A[p] = 3x^2}}}, so
{{{3x^2 = 3x^2 + 20x + 25 - 265}}}
Subtract {{{3x^2}}} from both sides
{{{20x - 240 = 0}}}
{{{20x = 240}}}
{{{x = 12}}}
{{{3x = 36}}}
The pool is 12m x 36m
check answer:
{{{x*3x = 12*36}}}
{{{A[p] = 432}}}
{{{A[d] + A[p] = 265 + 432}}}
{{{A[d] + A[p] = 697}}}, and, from above,
{{{A[d] + A[p] = 3x^2 + 20x + 25}}}
{{{A[d] + A[p] = 3*144 + 240 + 25}}}
{{{A[d] + A[p] = 432 + 265}}}
{{{A[d] + A[p] = 697}}}
OK