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.
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
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
4x + 10 -3x =2-3
To find all possible dimensions of Sam's cold frame with a volume of 120 feet cubed, we need to consider the factors of 120. Let's start by finding the factors of 120:
1 x 120 = 120
2 x 60 = 120
3 x 40 = 120
4 x 30 = 120
5 x 24 = 120
6 x 20 = 120
8 x 15 = 120
10 x 12 = 120
Now, let's express these factors in different orders to get all possible dimensions:
1ft x 120ft x 1ft
1ft x 1ft x 120ft
2ft x 60ft x 1ft
2ft x 1ft x 60ft
2ft x 40ft x 1ft
2ft x 1ft x 40ft
2ft x 30ft x 1ft
2ft x 1ft x 30ft
2ft x 24ft x 1ft
2ft x 1ft x 24ft
3ft x 40ft x 1ft
3ft x 1ft x 40ft
3ft x 30ft x 1ft
3ft x 1ft x 30ft
3ft x 24ft x 1ft
3ft x 1ft x 24ft
4ft x 30ft x 1ft
4ft x 1ft x 30ft
4ft x 24ft x 1ft
4ft x 1ft x 24ft
5ft x 24ft x 1ft
5ft x 1ft x 24ft
6ft x 20ft x 1ft
6ft x 1ft x 20ft
8ft x 15ft x 1ft
The list provided above consists of sixteen combinations with unique dimensions that can result in a volume of 120 feet cubed for Sam's cold frame.