You are wrapping a gift box that is 15 inches long, 12 inches wide, and 4 inches deep. Use a net to find the length and width of a single sheet of paper that could be used to wrap the entire gift box.

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To find the length and width of a single sheet of paper that can be used to wrap the entire gift box, we need to calculate the surface area of the box.

The surface area of the box is calculated by adding up the areas of all its sides. Since the gift box has a rectangular shape, it has six sides: the top, bottom, front, back, left, and right.

The formula to calculate the surface area of a rectangular prism (box) is:

Surface Area = 2(length × width) + 2(length × height) + 2(width × height)

Let's plug in the given dimensions of the box:
Length = 15 inches
Width = 12 inches
Height = 4 inches

Surface Area = 2(15 × 12) + 2(15 × 4) + 2(12 × 4)

Calculate each term:
2(15 × 12) = 2(180) = 360
2(15 × 4) = 2(60) = 120
2(12 × 4) = 2(48) = 96

Now, we can find the total surface area:
Surface Area = 360 + 120 + 96 = 576 square inches

To wrap the box with a single sheet of paper, we need a net that has a surface area greater than or equal to 576 square inches. A net is a 2-dimensional arrangement of the box's sides that can be unfolded to form the box.

We can start by finding the dimensions of the smallest net with a surface area greater than or equal to 576 square inches. We can do this by dividing 576 by different pairs of factors until we find a pair that yields a surface area greater than or equal to 576.

Let's try factor pairs:
(1, 576), (2, 288), (3, 192), (4, 144), (6, 96), (8, 72), (9, 64), (12, 48), (16, 36), (18, 32), (24, 24)

The closest pair that yields a surface area greater than or equal to 576 is (24, 24).

Hence, the length and width of a single sheet of paper to wrap the entire gift box would be 24 inches by 24 inches.