Arectangular swimming pool is 6ft deep. one side of the pool is 4.5 times longer than the other. the amount of water needed to fill the swimming pool is 1728 cubic feet. find the dimensions of the pool.

Set up two seperate equations
first the volume equation

1728=length*width*height
we know the height is 6ft

1728=L*W*6
divide both sides by 6 
288=L*W

then the second equation
L=4.5W 
if one side is 4.5 times larger

then take that and plug it back into the first equation
288=(4.5W)*W
288=(4.5)w^2

divide both sides by 4.5

64=w^2
so w=8

then plug that back into the last equation
L=4.5(8)
L=36