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Question

# Question 195 The floor of a room is 8 m 96 cm long and 6 m 72 cm broad. Find the minimum number of square tiles of the same size needed to cover the entire floor.

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Solution

## Given, length of the floor = 8 m 96 cm = 8 × 100 cm + 96 cm [ ∵ 1 m = 100 cm] = (800 +96) cm = 896 cm and breadth of the floor = 6 m 72 cm = 6 × 100 cm + 72 cm [ ∵ 1 m = 100 cm] = (600 + 72) cm = 672 cm Area of the floor = Length × Breadth = 896 × 672 cm2 Now, length of the square tile = HCF of 896 and 672 Prime factorization of 896 and 672 2896244822242112256228214771 267223362168284242321771 896=2×2×2×2×2×2×2×7 672=2×2×2×2×2×7×3 Common factors of 896 and 672=2×2×2×2×2×7=224 So, length of a square tile = HCF of 896 and 672 = 224 cm ∴ Minimum number of square tiles =Area of the floorArea of a square tile =896×672224×224=12 Hence, the minimum number of square tiles of the same size that is required to cover the entire floor is 12.

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