Exercise 34 Page 571

We want to find the width of the walkway, which is denoted in the problem as x. In order to do this we want subtract the area of the water from the area of the total pond — the water and walkway together. This will leave us with the area of the walkway. Area of walkway=Area of total pond - Area of water We will find values for these expressions from the problem and from the picture. First, we are told that the area of the walkway is 72 feet. We can substitute this in. 72=Area of total pond - Area of waterNext, to find the area of the total pond, we will use the picture.

Since the total pond is a rectangle, the area of a rectangle is length times width. We can see that the length of the total pond is x+8+x. This simplifies to 2x+8. From the diagram, we see that the width is x+6+x, which simplified is 2x+6. Let's multiply the length and width and substitute it into our equation. 72=(2x+8)(2x+6) - Area of water Now we will find the area of the water. Since the water is in a rectangle, we find the area by multiplying its length and width. We can see its length is 8 and its width is 6. Multiply the length and width and substitute it into our equation. 72=(2x+8)(2x+6) - (6)(8) Now we want to solve for x. Let's start by putting the equation in standard form.

Now, we can put our equation into factored form.

Our equation is now in factored form, so we can apply the Zero-Product Property.

We can see that x=2 or x=-9. Since x represents the width of a walkway, it would not make sense to have a negative value, so x=2 feet is the only correct answer.