The Kiddie Pool Area has a total area of 5000 square feet.

Question

rectangular pool and a rectangular concrete pad. The length of the rectangular pool is 30 feet greater than the width.

The pool has a concrete pad along only one side of the pool. The dimensions of the pad are 20 ft. by w feet, where w is the width of the pool.

 

Hint: First draw a picture of the pool and the concrete pad. Position the pad so that one side is along the width of the pool.

· Now label your picture with an expression for the total length, including the concrete pad. Label your picture with an expression for the total width.

Hint: Use substitution to label the length of the pool in terms of w.

· Using the expressions for total length and width, find an expression for total area of the rectangular pool and concrete pad. In order to solve for w, you will need to set the expression for area equal to the 5000 square feet. Now use your factoring skills to solve.

Hint: You will need to distribute the w and set the equation equal to zero in order to factor.

· Now that you have found the width of the pool, solve for the length. Again, sketch out a quick drawing of the Kiddie Pool Area with all dimensions labeled. This drawing will help you keep your measurements straight as you continue with the project.

Answer 1

Let the width of the pool be designated as W

The length of the pool L = W + 30

When one sketches out the rectangular pad along one side of the pool it adds

20 feet to the length so the length of the pool and pad together is W + 50

 

The dimensions of the pool and pad together is W by (W+50)

The total area is given by (length)(width) so the area of the pool and pad together is:

 

W(W+50) = 5000

W² + 50W = 5000

W² + 50W -5000 = 0

 

Lets factor this out... the factors of -5000 that will add to 50 are (100)(-50) so this gives us

 

(W+100)(W-50) = 0

This is only true if wither w + 100 = 0     or    W-50 = 0

Thus, the solution of the equation is W = -100 ft   or   W = 50 ft

 

We can discard W = -100ft since the pool will have positive dimensions so the width of the pool is 50ft

 

From this we can then get the length of the pool as W + 30 ....   So the length of the pool L = 80 ft

 

Thus the pool is 50ft x 80ft

The concrete pad is 50ft x 20ft