Greatest measuring length (in cm): Find the greatest possible length that can be used to measure exactly 7 m, 3 m 85 cm, and 12 m 95 cm. Give your answer in centimeters.

Introduction / Context:
The “greatest measuring length” that measures given lengths exactly is an HCF problem. Convert all quantities to a common unit and compute the HCF to ensure exact measurement without remainder.

Given Data / Assumptions:

• Lengths: 7 m, 3 m 85 cm, 12 m 95 cm.
• 1 m = 100 cm.
• Answer required in centimeters.

Concept / Approach:
Convert to centimeters, then find HCF. If L is the measuring unit, each length should be a multiple of L. The largest such L is HCF of the converted values.

Step-by-Step Solution:

Verification / Alternative check:
700/35 = 20, 385/35 = 11, 1295/35 = 37. All are integers, so 35 cm works.

Why Other Options Are Wrong:
15, 25, 42, and 21 cm are not the highest common measure; some may divide some lengths but not all, or are smaller than the true HCF.

Common Pitfalls:
Forgetting to convert meters to centimeters consistently, or stopping at an intermediate common factor (like 70) without checking against all lengths.

Final Answer:
35 cm