The greatest possible length that can be used to measure exactly the lengths 5 m 25 cm, 7 m 35 cm, and 4 m 90 cm is:

Explanation

To find the greatest possible length that can measure all three lengths exactly, we need to find the HCF (Highest Common Factor) of the given lengths. Convert each length to centimeters: 5 m 25 cm = (5 × 100) + 25 = 525 cm 7 m 35 cm = (7 × 100) + 35 = 735 cm 4 m 90 cm = (4 × 100) + 90 = 490 cm Step 1: Find the HCF of 525, 735, and 490 Using the Euclidean method or prime factorization: The prime factors of 525 are 5, 5, 3, and 7. So, 525 = 5 × 5 × 3 × 7. The prime factors of 735 are 5, 7, 7, and 3. So, 735 = 5 × 3 × 7 × 7. The prime factors of 490 are 5, 7, and 7, and 2. So, 490 = 5 × 7 × 7 × 2. The common factors are 5 and 7, so the HCF is 5 × 7 = 35. Answer: The greatest possible length that can be used to measure exactly the given lengths is 35 cm.