Please find the attached file for a better understanding of the solution provided here:
ABCD is the swimming pool and PQRS is the extent of the swimming pool plus the concrete walkway which is 6 yards wide.
Now, we know that the length is 8 yards shorter than twice it's width. Thus,
l=2w-8
Now the area of the region, A'B'QP will be: length x width. Now, the length here is l+6+6=2w-8+12=2w+4 and width is 6.
Thus, area of the region A'B'QP is (2w+4)x6=12w+24
Likewise, the area of the region D'C'RS will similarly be 12w+24 too.
Now, the area of the region BB'C'C will be 6 x w=6w
Similarly, the area of the region AA'D'D will be 6 x w=6w
Therefore, the total area of the walk way will be:
![2(12w+24)+2\times 6w=570](https://tex.z-dn.net/?f=%202%2812w%2B24%29%2B2%5Ctimes%206w%3D570%20)
![24w+48+12w=570](https://tex.z-dn.net/?f=%2024w%2B48%2B12w%3D570%20)
![36w+48=570](https://tex.z-dn.net/?f=%2036w%2B48%3D570%20)
![\therefore w=14.5](https://tex.z-dn.net/?f=%20%5Ctherefore%20w%3D14.5%20)
Therefore, length, l will be:
![l=2w-8=2\times 14.5-8=29-8=21](https://tex.z-dn.net/?f=%20l%3D2w-8%3D2%5Ctimes%2014.5-8%3D29-8%3D21%20)
Therefore, the dimensions of the swimming pool are:
Length, l= 21 yards and Width, w=14.5 yards