Answer:
[tex]46\ \text{feet}[/tex]
Step-by-step explanation:
Let width of the sidewalk be [tex]x[/tex]
Area of the sidewalk and pool is 1380 square feet
So
[tex](40+2x)(24+2x)=1380\\\Rightarrow 960+128x+4x^2=1380\\\Rightarrow 4x^2+128x-420=0\\\Rightarrow x=\frac{-128\pm \sqrt{128^2-4\times 4\left(-420\right)}}{2\times 4}\\\Rightarrow x=3,-35[/tex]
The width of the sidewalk is 3 feet.
The length of the side walk will be [tex]40+2x=40+2\times 3=46\ \text{feet}[/tex].
