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?

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#