Question

A rectangular deck has an area of 320 ft squared. The length of the deck is 4 feet longer than the width. Find the dimensions of the deck. Solve by completing the square.

Answer 1

So, the area of a rectangle is LxW. For this rectangle, LxW=320. We also know that the length is 4 feet longer than the width, that is L=W+4. With some substitution, we get (W+4)W=320. Simplify to get W^2+4w=320. Now the fun part! When we complete the square, we'll end up with (W+___)^2, right? So, let's take half of 4, which is 2, and square it. That's 4. Add that 4 to what we already have:

W^2+4W+4. But remember, what we do to one side of an equation we must do to the other side. So we really have W^2+4W+4=320+4.

We simplify and get W^2+4W+4=324. Factor the left side of the equation and get (W+2)^2=324. When we take the square root of both sides of the equation we get W+2=18, so W=16, which means the length (4 ft longer) is 20 ft.

Verify

w•l=320

16•20=320✔️

Explanation:

Answer 2

So, the area of a rectangle is LxW. For this rectangle, LxW=320. We also know that the length is 4 feet longer than the width, that is L=W+4. With some substitution, we get(W+4)W=320. Simplify to get W^2+4w=320. Now the fun part! When we complete the square, we'll end up with (W+___)^2, right? So, let's take half of 4, which is 2, and square it. That's 4. Add that 4 to what we already have:W^2+4W+4. But remember, what we do to one side of an equation we must do to the other side. So we really have W^2+4W+4=320+4.We simplify and get W^2+4W+4=324. Factor the left side of the equation and get(W+2)^2=324. When we take the square root of both sides of the equation we getW+2=18, so W=16, which means the length (4 ft longer) is 20 ft. Do you have questions about the completing the square part? In a trinomial, the coefficient in the x term is the sum of the two factors and the constant term is the product. So, in the completing the square, you have the sum of a number added to itself or 2 times that factor. That's why we take half of it. Then, we square it to get the constant term. Square completed. But don't forget to keep the balance in the equation by also adding the constant term to the other side.