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.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: 7 m = 700 cm3 m 85 cm = 385 cm12 m 95 cm = 1295 cmHCF(700, 385) ⇒ 700 − 385 = 315; HCF(385, 315) = 70; thus HCF so far = 70HCF(70, 1295) ⇒ 1295 mod 70 = 35 ⇒ HCF = 35Therefore, the greatest measuring length is 35 cm. 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

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.

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