what lengths are possible for piece cut from the 12-cm piece of string ?
0 < L < 12
its 4, 2, 6, 1, 12, and 3 hope this helps!!
To determine the possible lengths of the pieces cut from a 12-cm piece of string, we need to consider the range of lengths that can be obtained through cutting.
When cutting a string, the two pieces produced will have lengths that sum up to the original length. Let's assume that the first piece has a length of "x" cm. Therefore, the second piece will have a length of "12 - x" cm.
Since we want to find all possible lengths, we need to consider all possible values of "x" and then calculate the corresponding length of the second piece.
To start, let's look at the extremes. The shortest possible length for the first piece is 0 cm, which would mean the second piece should be the entire 12 cm string. On the other hand, the longest possible length for the first piece is 12 cm, which would result in a second piece of 0 cm.
So, the possible lengths for the first piece range from 0 cm to 12 cm. For each value of "x," we can calculate the length of the second piece by subtracting "x" from 12.
Therefore, the possible lengths for the pieces when cut from a 12-cm string are:
- First piece: 0 cm, Second piece: 12 cm
- First piece: 1 cm, Second piece: 11 cm
- First piece: 2 cm, Second piece: 10 cm
- ...
- First piece: 12 cm, Second piece: 0 cm
Note that these are all the possible combinations, as any length between 0 cm and 12 cm can be chosen for the first piece, resulting in the corresponding length for the second piece.