The greatest possible length which can be used to measure exactly the lengths…

To find the greatest possible length that can measure different lengths exactly, you need to find the Highest Common Factor (H.C.F.) of those lengths. The first step is to ensure all measurements are in the same unit.

Step-by-Step Calculation

1. Convert all lengths to centimeters:

• 7 m = 700 cm

• 3 m 85 cm = 385 cm

• 12 m 95 cm = 1295 cm

2. Find the H.C.F. of 700, 385, and 1295:

• Prime factorization:

  • 700 = 2² × 5² × 7¹

  • 385 = 5¹ × 7¹ × 11¹

  • 1295 = 5¹ × 7¹ × 37¹

• The common prime factors present in all three are 5 and 7.

• H.C.F. = 5 × 7 = 35 cm.