Answer:
5 feet
Step-by-step explanation:
We are given that
Width of rectangular pool=b=30 feet
Length of rectangular pool=l=40 feet
Area of rectangle=[tex]l\times b[/tex]
Using the formula
Area of rectangular pool=[tex]30\times 40=1200ft^2[/tex]
Total area enclosed within the perimeter of the deck=[tex]2000ft^2[/tex]
Width of deck=x ft
Length of rectangular pool including wooden deck=40+2x ft
Width of rectangular pool including wooden deck=30+2x ft
Area of rectangular pool including wooden deck=[tex](40+2x)(30+2x)[/tex]
According to question
[tex](40+2x)(30+2x)=2000[/tex]
[tex]40(30)+2x(30)+40(2x)+2x(2x)=2000[/tex]
[tex]1200+60x+80x+4x^2=2000[/tex]
[tex]140x+4x^2=2000-1200=800[/tex]
[tex]4x^2+140x-800=0[/tex]
[tex]x^2+35x-200=0[/tex] (Dividing by 4 on both sides)
[tex]x^2+40x-5x-200=0[/tex]
[tex]x(x+40)-5(x+40)=0[/tex]
[tex](x+40)(x-5)=0[/tex]
[tex]x+40=0[/tex]
[tex]x=-40[/tex]
It is not possible because width cannot be negative it is always natural number.
[tex]x-5=0\implies x=5[/tex]
Hence, the width of the deck=5 ft
