Exercise 27 Page 571

We have a rectangular blanket with an area of 24 square feet. We want to find the length and width of the blanket. Recall the area of a rectangle is length times width. A= l w ⇒ 24= l w We know that the length should be 2 feet longer than the width. We can call the width x. This makes the length is x+2. Let's rewrite our area formula using these values. 24=( x+2)( x) ⇒ 24=( x+2)( x)We now have an equation with one variable. If we can solve for the width x we can find the length. Let's start by putting our equation in standard form.

Now, we can factor the right hand side of the equation so that we can apply the Zero-Product Property.

Now that the equation is in factored form, let's apply the Zero Product Property.

We can see that x=- 6 and x=4. However, recall that x represents width. Since it does not make sense to have a negative value as a width, x=4 is the only correct value. Now that we have width, we can solve for length.

We have found that the width of the rectangle is 4 feet and the length is 6 feet.