Find the greatest possible length that exactly measures 7 m, 3 m 85 cm, and 12 m 95 cm.

Given data

• Lengths: 7 m, 3 m 85 cm, 12 m 95 cm.

Concept / Approach

• Convert to a common unit (centimetres), then compute the H.C.F. of the lengths.

Step-by-step conversion & H.C.F.

7 m = 700 cm3 m 85 cm = 385 cm12 m 95 cm = 1295 cmHCF(700, 385) ⇒ 700 − 385 = 315; 385 − 315 = 70; 315 ÷ 70 = remainder 35; 70 ÷ 35 = 0 ⇒ HCF = 35.HCF(35, 1295): 1295 ÷ 35 = 37 remainder 0 ⇒ HCF remains 35.Hence greatest exact measuring length = 35 cm (i.e., 0.35 m).

Verification

700/35 = 20; 385/35 = 11; 1295/35 = 37 ⇒ all integers.

Common pitfalls

• Mixing metres and centimetres during H.C.F. computation.
• Accidentally taking L.C.M. instead of H.C.F.

Final Answer

Greatest length: 35 cm.