The Robertsons put a rectanglar pool in their backyard with a stone walkway around it.The total length of the pool and walkway is 3 times the total width.

Question

The walkway is 2 ft wide.

a. Write an expression for the area of the pool.

 

b.Find the area of the pool when the total width is 10 ft.

 

c. Find the area of the pool when the total width is 9 ft.

Answer 1

Since the walkway is 2ft on all sides, we have 4ft of walkway for each of length L, and width W

 

We know that total length L = 3(total width W), or L = 3W.

 

Hence the length of the pool l = L - 4, and the width of the pool w = W - 4

 

a) area of the pool is length times width, but each of these has the 4 ft of walkway to consider (as described above):

 

A = lw

A = (L - 4)(W - 4)

A = [(3W) - 4](W - 4)

A = (3W - 4)(W - 4)

A = 3W(W - 4) - 4(W - 4)

A = 3W² - 16W + 16

 

b) if the total width W = 10, then the area of the pool is:

 

A = 3(10)² - 16(10) + 16

A = 3(100) - 160 + 16

A = 316 - 160

A = 156 ft²

 

c) if the total width W = 9, then the area of the pool is:

 

A = 3(9)² - 16(9) + 16

A = 3(81) - 144 + 16

A = 243 - 144 + 16

A = 115 ft²