Final answer:
To find the number of linear feet of crown molding needed, you need to calculate the perimeter of the ceiling. By assigning a variable to the width of the room, you can express the length in terms of the width. Solving a quadratic equation will help you find the width, and then you can calculate the perimeter of the ceiling. The answer is 52 linear feet of crown molding.
Step-by-step explanation:
To find the length of the room, we can assign a variable. Let's say the width of the room is x. Since the length is six feet longer than the width, we can express the length as x + 6. The area of the ceiling is the product of the length and width, so we have (x + 6) * x = 160. Simplifying this equation, we get x^2 + 6x - 160 = 0. Solving this quadratic equation, we find the width of the room (x) to be 10 feet. To calculate the perimeter of the ceiling, we add the length of all four sides, which are two lengths and two widths. The perimeter is 2(x + 6) + 2x = 4x + 12. Plugging in the width we found, the perimeter is 4(10) + 12 = 52 feet. Therefore, you should buy 52 linear feet of crown molding to completely decorate the perimeter of your ceiling.