Floor tiling – Least number of square tiles (HCF approach): A room 5 m 44 cm long and 3 m 74 cm broad is to be paved with identical square tiles. Find the least number of square tiles required (use consistent units).

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

Accepted Answer

Introduction / Context:To minimise the number of square tiles covering a rectangle without cutting, choose the largest possible tile that exactly divides both dimensions, i.e., the HCF of the side lengths (in the same unit). Given Data / Assumptions: Length = 5 m 44 cm = 544 cm. Breadth = 3 m 74 cm = 374 cm. Concept / Approach:Tile side = HCF(544, 374). Number of tiles = (544 × 374) / (HCF^2). Step-by-Step Solution: Compute HCF(544, 374). 544 = 374*1 + 170; 374 = 170*2 + 34; 170 = 34*5 + 0 ⇒ HCF = 34 cm.Number of tiles = (544 × 374) / (34 × 34).544/34 = 16; 374/34 = 11 ⇒ tiles = 16 × 11 = 176. Verification / Alternative check:Try any larger tile side (>34 cm): it will not divide at least one dimension; using smaller sides increases count. Why Other Options Are Wrong:136, 146, 166 arise from incorrect HCF or arithmetic; 176 is exact. Common Pitfalls:Not converting metres to centimetres consistently; computing LCM instead of HCF; arithmetic slips. Final Answer:176

Floor tiling – Least number of square tiles (HCF approach): A room 5 m 44 cm long and 3 m 74 cm broad is to be paved with identical square tiles. Find the least number of square tiles required (use consistent units).

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