Question

Bill Gates wants to construct an in ground swimming pool for his dog. he wants it's length to be 8 yards shorter than twice it's width. he then wants to surround it with a concrete walkway 6 yards wide. he can only afford 570 square yards of concrete. what should the dimensions be of the pool ?

Answer 1

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:

$2(12w+24)+2\times 6w=570$

$24w+48+12w=570$

$36w+48=570$

$\therefore w=14.5$

Therefore, length, l will be:

$l=2w-8=2\times 14.5-8=29-8=21$

Therefore, the dimensions of the swimming pool are:

Length, l= 21 yards and Width, w=14.5 yards

Answer 2

The dimensions of the pool should be 34