Find the side of the largest square slab which can be paved on the floor of a…
2024
Find the side of the largest square slab which can be paved on the floor of a room 5 meters 44cm long and 3 meters 74 cm broad.
- A.
56 cm
- B.
42 cm
- C.
38 cm
- D.
34 cm
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Step 1: Convert the room dimensions to centimetres: 5 m 44 cm = 544 cm, 3 m 74 cm = 374 cm.
Step 2: The largest square slab must have a side length that exactly divides both lengths, so we need the greatest common divisor (HCF) of 544 and 374.
Apply the Euclidean algorithm: 544 − 374 = 170 (so 544 mod 374 = 170).
Next step: 374 − 2 × 170 = 34 (so 374 mod 170 = 34).
Finally: 170 mod 34 = 0, so the HCF is 34.
Alternative verification (prime factors):
544 = 2 × 2 × 2 × 2 × 2 × 17 = 2^5 × 17
374 = 2 × 17 × 11
Common factors are 2 and 17, so their product is 2 × 17 = 34, matching the Euclidean result.
Answer: The side of the largest square slab that can pave the floor is 34 cm.