Question

Find the least number of square tiles required to pave the ceiling of a room $15m17cm$ long and $9m2cm$ broad.

Answer 1

Step 1: Calculate the area of the ceiling

Length of the ceiling $=15m17cm=1517cm$

Width of the ceiling $=9m2cm=902cm$

$\therefore$Area of the ceiling $=1517\times 902=1368334c{m}^2$

Step 2: Find the area of square tile

The dimension of square tile required to pave the ceiling $=$HCF of $(1517,902)$ $=41$

$\therefore$ Area of the square tile $=41\times 41=1681c{m}^2$

Step 3: Find the number of square tiles required

Number of square tiles required $=\frac{AreaofCeiling}{Areaoftile}=\frac{1368334}{1681}=814$

Hence, the least number of square tiles required to pave the ceiling of a room is $\mathbf{814}$.