A pizza box with a square base is to be made rom a rectangular sheet of cardborad by cutting six 1-inch squares from the corners and the middle sections and folding up the sides. If area of the base is to be 144 in^2, what piece of cardboard should be used?
To solve this problem, we first need to understand the concept of the pizza box construction. By cutting squares from the corners and middle sections of the cardboard, we create flaps that can be folded up to form the sides of the pizza box. The resulting shape will have a square base and flaps on all four sides.
Let's denote the length of the original rectangular sheet of cardboard as "x" inches. Since we cut 1-inch squares from both ends of the cardboard, the length of the resulting base will be reduced by 2 inches (1 inch from each end), resulting in a square with a side length of (x - 2) inches.
Now, we can calculate the area of the base by squaring the side length:
Area of the base = (side length)^2 = (x - 2)^2
According to the problem, the area of the base is given as 144 in^2. Setting up the equation, we have:
144 = (x - 2)^2
To solve for x, we can take the square root of both sides of the equation:
sqrt(144) = x - 2
Simplifying, we have:
12 = x - 2
Adding 2 to both sides, we get:
x = 14
Therefore, the original rectangular sheet of cardboard should have dimensions of 14 inches by the original width.