The length of a rectangular pool is 2 feet less than twice the width. If the area of the poet is 264 ft^2. What are the dimensions of the pool?

1 Answer

The width is 12 feet and the length is 22 feet.

Explanation:

To answer the question the key is to translate the information into mathematical language.

So we have a rectangular pool, with a length l and a width w. The first sentence says that l is 2 feet less than 2w, so this condition can be translated into
l=2w-2
Then we know the area A=264 of the pool, which is a rectangle and so the area can be computed by multiplying the length by the width: A=l*w. We get a second condition on l and w:
l*w=264

Now we can plug the first condition into the second, substituting l:
(2w-2)w=264
2w^2-2w-264=0
w^2-w-132=0

Now we use the quadratic formula and get
w=(1 pm sqrt(1+4*132))/2=(1 pm sqrt(529))/2=(1 pm 23)/2

Since we deal with positive numbers (width can't be negative), we have to reject w=-11 and we get w=12. Now using the first condition we get l:
l=2 * 12 -2 = 24-2=22