Paul has 3 pieces of rope of length 36cm,40cm,and 48cm respectively. He needs to select 2 out of the 3 pieces and cut them into smaller pieces of equal length. What is the greatest possible length of each smaller piece if there is to be no wastage?
why wouldn't he take the longest two, cut them into 36cm pieces?
I'd say it's because they are to be cut from 2 of the pieces. That is, which two ropes have the largest common factor?
36 = 12*3
40 = 8*5
48 = 12*4
Looks to me like 12cm is the longest piece that divides evenly 2 of the 3 original lengths.
To find the greatest possible length of each smaller piece without any wastage, we need to find the greatest common divisor (GCD) of the three rope lengths. The GCD represents the largest length that can be evenly divided into all the given lengths.
To calculate the GCD, we can use the euclidean algorithm:
Step 1: Begin by comparing the smallest and largest lengths, which are 36cm and 48cm. We can find the remainder by dividing 48cm by 36cm, which gives us 12cm (48cm - 36cm).
Step 2: Now compare the remainder (12cm) with the remaining length, which is 40cm. Again, we find the remainder by dividing 40cm by 12cm, which gives us 4cm (40cm - 3*12cm).
Step 3: Finally, compare the latest remainder (4cm) with the smallest length, which is 36cm. Divide 36 by 4 to get a remainder of 0, indicating that 4cm is the GCD of the three lengths.
Therefore, the greatest possible length of each smaller piece with no wastage is 4cm.