*15 points* The volume of a rectangular box is 2,592 cubic centimeters. The height of the box is 18 cm. What are the possible length and width of the box? ​

Step-by-step explanation:

V = length * height * width = 18 * length * width

2,592 = 18 * length * width ; divide both sides by 18

144=  length * width ; now what 2 numbers multiplied are giving us 144?

1*144 = 144 ; 2*72 = 144 ; 3*48=144 ; 4*36 =144 ; 6*24 = 144 ; 8*18 = 144 ;

9*16 =144 ; 12*12 =144

5, 7, 10 and 11 does not divide 144 into a whole number

possible lengths and widths are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

312312

step-by-step explanation: