Question

Sam's cold frame has a volume of 120 feet cubed. List all the possible dimensions of the cold frame. Use only whole numbers and use any combination of numbers once. For example, if you list 1ft*8ft*15ft, you may not list 1ft*15ft*8ft or 8ft*1ft*15ft, and so on. Try to find sixteen combinations.

List all the answers please.

Answer 1

Break 120 up into a product of prime numbers. Then break that list into as many combinations of three numbers as you can think of, using all of the numbers. Examples:
120 = 1*2*2*2*3*5
= 1*(2*2*2)*(3*5)= 1x8x15
= 2*(2*2)*(3*5)= 2x4x15
= 1*2*(2*2*3*5)=1x2x60
= (2*2)(2*3)*5= 4x6x5
= 2*(2*5)*(2*3)=2x10x6
etc

Answer 2

120 = 2*2*2*3*5

So we need triples of these that multiply to get 120, but we must not forget that 1 can also be used.
So I went about it sort of systematically

1,1,120 ----- only case with 2 ones
1,2,60
1,3,40
1,4,30
1,5,24
1,6,20
1,8,15
1,10,12 --- to got more would repeat some

2,2,30
2,3,20
2,4,15
2,5,12
2,6,10

4,3,10
4,5,6

8,3,5

Done, 16 of them

Answer 3

4x + 10 -3x =2-3