Find the greatest possible length of a rope which can be used to measure exactly the lengths 7m, 3m 85cm and 12m 95cm.

First turn them all into cm: 70cm, 385cm, and 1295cm.

Then find the Greatest Common Factor (the largest number all three numbers as indicated above can divide through evenly with out a decimal). In this case the number is 35.

GCF =5

To find the greatest possible length of the rope that can measure the given lengths, we need to find the greatest common divisor (GCD) of the lengths.

Step 1: Convert all the lengths to the same unit.
7m = 700cm
3m 85cm = 385cm
12m 95cm = 1295cm

Step 2: Find the GCD of the converted lengths.
To find the GCD, we can use the Euclidean algorithm.

GCD(700, 385) = GCD(385, 315)
GCD(385, 315) = GCD(315, 70)
GCD(315, 70) = GCD(70, 35)
GCD(70, 35) = GCD(35, 0)

The GCD is 35.

Step 3: Convert the GCD back to meters and centimeters.
35cm = 0.35m

So, the greatest possible length of the rope that can be used to measure exactly 7m, 3m 85cm, and 12m 95cm is 0.35m or 35cm.