Answer:
Greatest number of pieces = 5
Pieces are 3 cm, 4 cm, 5 cm, 6 cm and 7 cm
Step-by-step explanation:
To find - You have 25 cm piece of ribbon. How many cuts do you need to make to obtain the greatest number of pieces, where each piece is a different length and the length of each piece is a whole number, in centimeters.
Proof -
If we cut the pieces in 1 part, then the ribbon cut into
1 + 24 , 2 + 23 , 3 + 22, 4 + 21, 5 + 20, 6 + 19, 7 + 18, 8 + 17, 9 + 16, 10 + 15, 11 + 14, 12 + 13
If we cut the pieces in 2 part, then the ribbon cut into
1 + 2 + 22, 1 + 3 + 21, and so on
The same process is going on
After that, we get
The greatest number of pieces will be 5 and the cut we make on the ribbon is 3 + 4 + 5 + 6 + 7
∴ we get
Greatest number of pieces = 5
Pieces are 3 cm, 4 cm, 5 cm, 6 cm and 7 cm
