The volume of a rectangular prism is 280cm cubed and the height is 8cm. Which of the following could be the dimensions of the length and the width?

What following?

To find the dimensions of the length and width of a rectangular prism, we need to use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

Given that the volume of the rectangular prism is 280 cm^3 and the height is 8 cm, we can substitute these values into the formula:

280 = Length x Width x 8

To solve for the dimensions of the length and width, we need to find two numbers that multiply to give 280 when multiplied by 8. Let's list the factors of 280:

Factors of 280: 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

Now, we divide 280 by each factor to find the corresponding factor pairs:

280 ÷ 1 = 280
280 ÷ 2 = 140
280 ÷ 4 = 70
280 ÷ 5 = 56
280 ÷ 7 = 40
280 ÷ 8 = 35
280 ÷ 10 = 28
280 ÷ 14 = 20
280 ÷ 20 = 14
280 ÷ 28 = 10
280 ÷ 35 = 8
280 ÷ 40 = 7
280 ÷ 56 = 5
280 ÷ 70 = 4
280 ÷ 140 = 2
280 ÷ 280 = 1

From these factor pairs, we can see that the possible combinations of the length and width are:

1) Length = 280, Width = 1
2) Length = 140, Width = 2
3) Length = 70, Width = 4
4) Length = 56, Width = 5
5) Length = 40, Width = 7
6) Length = 35, Width = 8
7) Length = 28, Width = 10
8) Length = 20, Width = 14
9) Length = 14, Width = 20
10) Length = 10, Width = 28
11) Length = 8, Width = 35
12) Length = 7, Width = 40
13) Length = 5, Width = 56
14) Length = 4, Width = 70
15) Length = 2, Width = 140
16) Length = 1, Width = 280

So, any of the above 16 combinations of lengths and widths could be the dimensions for the given volume of 280 cm^3 and height of 8 cm.