The Smiths’ have decided to put a paved walkway of uniform width around their swimming pool. The pool is a rectangular pool that measures 12 feet by 20 feet. The area of the walkway will be 68 square feet. Find the width of the walkway.

 

• know how to solve quadratic equations
• know formulas for finding the area of geometric figures
• know how to multiply polynomials
• write and solve an equation for the problem

The Smith’s have a rectangular pool that measure 12 feet by 20 feet. They are building a walkway around it of uniform width. First we need to draw a picture as illustrated in the figure below:

 

 

Next we need to write an equation.

 

Let x be the width of the walkway that will surround the pool. There are three rectangles in this picture on which we need to focus: the larger rectangle, the pool itself, and the rectangle that represents the walkway around the pool. Our equation will include the area of all three rectangles.

 

The length of the larger rectangle is , which simplifies to

 

length_{larger rectangle} =

 

The width of the larger rectangle is , which simplifies to

 

width_{larger rectangle} =

 

The area for the larger rectangle then becomes

 

area_{larger rectangle} =

 

The pool itself has an area of square feet.

 

The rectangle that wraps around the pool is given to be 68 square feet.

By putting all three of these areas together, we know that the area of the larger rectangle is equal to the area of the pool plus the area of the walkway that surrounds the pool. So our equation becomes:

 

 

Finally, we need to solve this equation to find the width of the walkway.

 

	Rearrange the terms for easier multiplication and find the sum of 68 and 240.
	Multiply the binomials.
	Combine like terms and subtract 308 from each side.
	Factor.
	Solve each factor.
	Since dimensions of a pool and a walkway around a pool cannot be negative our answer is that the width of the walkway is 1 foot.
x = 1

 

If regional building codes require that the walkway be 6 inches thick, how many square yards of cement must they purchase to complete the project?(concrete facts courtesy of  Do It Yourself.com)

 

The volume of cement needed in cubic feet is (68 ft²)(6/12 ft) = 34 ft³

 

A typical 60-pound bay of pre-mixed concrete costs between $1.35-$1.80 and yields one-half of a cubic foot. They would need a minimum of 68 bags to complete the project: 68 x $1.80 = $122.40 plus a strong back.

 

One cubic yard equals (1 yd)³ = (3 ft)³ = 27 ft³, so they will need 34 ft³/27 ft³ = 1.26 yd³.

 

A fully-loaded cement truck carries 10 cubic yards at an average price of $65 per cubic yard PLUS $17 per cubic yard short of the truck's full capacity. Since concrete is only sold in increments of full yards, no fractions, their cost would be $65 + $17(8) = $265.