The statement says two important facts:
The length is 8 more than double the width, and the area is equal to 960 ft^2. So rewrite these facts in equations:
Remember that the pool must be rectangular
[tex]l=8+2w[/tex][tex]A=l*w[/tex][tex]l*w=960[/tex]
Put the variables on the same side, so reach the next two equations:
[tex]l-2w=8[/tex][tex]l*w=960[/tex]
Now solve one for l, you can choose any equation and any variable, I will clear l from the first equation:
[tex]l=8+2w[/tex]
Now replace in the second equation and solve
[tex](8+2w)*w=960[/tex][tex]2w^2+8w=960[/tex][tex]2w^2+8w-960=0[/tex][tex]w_{1,\:2}=\frac{-8\pm \sqrt{8^2-4\cdot \:2\left(-960\right)}}{2\cdot \:2}[/tex][tex]w_{1,\:2}=\frac{-8\pm \:88}{2\cdot \:2}[/tex][tex]w_{1,\:2}=\frac{-8\pm \:88}{2\cdot \:2}[/tex][tex]w_1=\frac{-8+88}{2\cdot \:2},\:w_2=\frac{-8-88}{2\cdot \:2}[/tex][tex]w=20,\:w=-24[/tex]
We only choose the positive value, so the width is 20 ft
Now replace in the first equation to find the length:
[tex]l=8+2(20)=8+40=48[/tex]
So the answer is:
length= 48ft
width=20ft
