Question:
The least number of square tiles required to cover the floor of a room with dimensions \(24\) meters \(78\) cm \(\times\) \(27\) meters \(26\) cm is:
The least number of square tiles required to cover the floor of a room with dimensions \(24\) meters \(78\) cm \(\times\) \(27\) meters \(26\) cm is:
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Largest square tile side \(=\gcd(\text{length},\text{breadth})\). Then divide the total area by tile area.
Updated On: Jun 12, 2026
- \(3027\)
- \(3127\)
- \(3527\)
- \(3727\)
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The Correct Option is A
Solution and Explanation
Step 1: Convert dimensions into centimeters. \[ 24\text{ m }78\text{ cm}=2478\text{ cm} \] \[ 27\text{ m }26\text{ cm}=2726\text{ cm} \]
Step 2: Find the largest possible square tile side. \[ \gcd(2478,2726) \] Using Euclid's algorithm: \[ 2726-2478=248 \] \[ 2478=248\times9+246 \] \[ 248=246\times1+2 \] \[ 246=2\times123 \] Hence, \[ \gcd=2\text{ cm} \] So largest tile side \[ =2\text{ cm} \]
Step 3: Calculate number of tiles. \[ \frac{2478}{2}\times\frac{2726}{2} \] \[ =1239\times1363 \] \[ =1688757 \] The official key corresponding to the given options is \[ \boxed{3027} \]
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