The length and breadth(width) of the pool are
[tex]l\approx15.7m\text{ and }b\approx7.7m[/tex]
Let
[tex]l=\text{length of the side of the pool}\\b=\text{breadth of the pool side}\\w=\text{the width of the strip of deck surrounding the pool}[/tex]
From the question, we can build the following relationships
[tex]l+2w=20\\b+2w=12[/tex]
subtracting to eliminate [tex]w[/tex] (we do not even need it!)
[tex]l-b=8\\b=l-8[/tex]
we can also build another relationship from the question. Since the area of the strip equals the area of the pool:
[tex]lb+lb=2lb=20\times 12\\lb=120[/tex]
We have two unknowns, [tex]l[/tex] and [tex]b[/tex]. Eliminate [tex]b[/tex]
[tex]lb=120\\l(l-8)=120\\l^2-8l-120=0[/tex]
If we solve the quadratic equation for [tex]l[/tex], we get
[tex]l=4+2\sqrt{34}\approx 15.7m[/tex]
and
[tex]b=l-8\\b=(4+2\sqrt{34})-8\\b=2\sqrt{34}-4\approx7.7m[/tex]
The length and breadth(width) of the pool are
[tex]l\approx15.7m\text{ and }b\approx7.7m[/tex]
Learn more about area here: https://brainly.com/question/1447350
