Answer:
To avoid cutting out a fraction of an inch, we need to choose a value of x that is a factor of both 36 inches and 48 inches, since those are the lengths of the sides of the rectangular sheet of cardboard we are using.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The largest factor that both 36 and 48 have in common is 12. However, we can't choose x to be 12 inches because that would mean the length and width of the rectangular box would also be 12 inches, which is too small for our purposes.
Therefore, we should choose x to be the next largest factor that both 36 and 48 have in common, which is 6 inches. This means we will cut six 6-inch by 8-inch rectangles from the cardboard sheet.
The dimensions of the rectangular box will be:
Length = 2x + 2h = 2(6 in) + 2(8 in) = 12 in + 16 in = 28 in
Width = 2x + 2w = 2(6 in) + 2(12 in) = 12 in + 24 in = 36 in
Height = h = 8 in
Therefore, the dimensions of the rectangular box are 28 inches by 36 inches by 8 inches