Question

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

Answer 1

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`