Question

You want to put crown molding in your living room. You know that the area of your ceiling is 160 ft2 and the length of the room is six feet longer than the width. How many linear feet of crown molding should you buy to completely decorate the perimeter of your ceiling?

Answer 1

To determine the amount of crown molding needed for the room's perimeter, the width and length of the room are calculated using the area provided. After solving the quadratic equation, the dimensions are found, and the perimeter of the room is 52 feet, which equals the linear feet of crown molding required.

Step-by-step explanation:

To find out how many linear feet of crown molding you need to buy to decorate the perimeter of your ceiling, we must first establish the dimensions of the room. Since we know that the area of the ceiling is 160 square feet, and the length is six feet longer than the width, we can set up an equation to solve for the dimensions.

Let w represent the width of the room. Thus, the length will be w + 6 feet. The area of the room is given by the formula A = length × width, which means 160 = w × (w + 6).

Now we solve the quadratic equation:

• w^2 + 6w - 160 = 0

By factoring or using the quadratic formula, we find that w = 10 and l = 16 (disregarding the negative solution since a negative width does not make sense for room dimensions).

Now that we have the width and the length of the room, we can find the perimeter by adding twice the length and twice the width:

Perimeter = 2 × length + 2 × width

Perimeter = 2 × 16 + 2 × 10

Perimeter = 32 + 20

Perimeter = 52 feet

Therefore, you should buy 52 linear feet of crown molding to decorate the perimeter of your ceiling. Remember to consider extra material for corners and possible mistakes.