1. ## Rational Function..word problem..HELP!!!

OK heres the problem:

Designing a Swimming Pool
Thompson Recreation, Inc., wants to build a rectangular swimming pool with the top of the pool having surface are 1000ft squared. The pool is required to have a walk of uniform width 2 ft surrounding it. Let x be the length of one side of the pool.

a.Express the area of the plot of land needed for the pool and surrounding sidewalk as a function of x.

b.Find the dimensions of the plot of land that has the least area. What is the least area?

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2. ## Area problem

Hello FabulousMuah
Originally Posted by FabulousMuah
OK heres the problem:

Designing a Swimming Pool
Thompson Recreation, Inc., wants to build a rectangular swimming pool with the top of the pool having surface are 1000ft squared. The pool is required to have a walk of uniform width 2 ft surrounding it. Let x be the length of one side of the pool.

a.Express the area of the plot of land needed for the pool and surrounding sidewalk as a function of x.

b.Find the dimensions of the plot of land that has the least area. What is the least area?
(a) If the sides of the rectangle measure $x$ feet and $y$ feet, then its area is $xy$ square feet.

So $xy = 1000$

So $y$ = what, in terms of $x$?

Now, there's a $2$ foot wide path all the way around the pool. So the lengths of the sides of the whole rectangular plot are $(x+4)$ feet and (what)? feet.

Now multiply these two lengths to get the area of the whole plot. This is the function you need.

(b) You'll probably use calculus to find the value of $x$ for which this function is a mimimum. (Or you could get an approximate value by drawing a graph.)

Can you see how to do it now?