Final answer:
To find the dimensions of the cardboard needed to create the box, we establish an equation using the box's volume (104 in³), the cut squares (4 in), and that the length is 11 inches more than the width. The correct dimensions are a width of 4 inches and a length of 15 inches, corresponding to answer choice d.
Step-by-step explanation:
To calculate the dimensions of the piece of cardboard needed to construct the box, we should start by setting up an equation based on the given information. The volume of the box is 104 cubic inches, and the sides of the squares cut out from each corner are 4 inches. Therefore, if we denote the width of the cardboard as w inches, then the length would be w + 11 inches.
After the square corners are cut out and the sides are folded up to create the box, the actual width and length of the base of the box will be reduced by 8 inches (4 inches from each side). Therefore, the base dimensions of the box are (w - 8) inches for the width and (w + 11 - 8) inches for the length, or (w + 3) inches for the length.
The height of the box will be 4 inches (the size of the cutout squares). We can now write the equation for the volume of the box:
Volume of the box = (width of base) x (length of base) x (height)
Substituting the values we have:
104 in³ = (w - 8) in x (w + 3) in x 4 in
Simplifying and solving for w will give us the width of the cardboard and w + 11 for the length. By solving the quadratic equation, we find that the possible dimensions for the cardboard are Length: 15 inches, Width: 4 inches, which corresponds to answer choice d.