A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marble tiles 20 cm × 20 cm, the number of tiles required to cover the path is (M.A.T., 2007)

### Concept & Area Division To find the number of tiles required, divide the total area of the path by the area of a single tile. Ensure all measurements are in the same units (either meters or centimeters). $$ \text{Number of Tiles} = \frac{\text{Total Path Area}}{\text{Area of One Tile}} $$ ### Step-by-Step Solution * Given: Inner length $l = 24$ m, Inner width $b = 14$ m. Path width $w = 1$ m (outside). * The outer dimensions of the garden including the path are $(24 + 2) = 26$ m and $(14 + 2) = 16$ m. * Outer Area = $26 \times 16 = 416\text{ m}^2$. * Inner Area (Garden) = $24 \times 14 = 336\text{ m}^2$. * Path Area = Outer Area - Inner Area = $416 - 336 = 80\text{ m}^2$. * Convert tile dimensions to meters: $20\text{ cm} = 0.2\text{ m}$. Area of one tile = $0.2 \times 0.2 = 0.04\text{ m}^2$. * Number of tiles = $80 / 0.04 = 8000 / 4 = 2000$. ### Exam Strategy & Shortcut Use the direct outer path area formula: $2w(l + b + 2w) = 2(1)(24 + 14 + 2) = 2(40) = 80\text{ m}^2$. Convert to $\text{cm}^2$: $80 \times 10000 = 800000\text{ cm}^2$. Tile area in $\text{cm}^2$ is $20 \times 20 = 400$. Divide: $800000 / 400 = 2000$. ### Common Pitfall Forgetting to convert the tile dimensions from centimeters to meters (or path from meters to centimeters), resulting in wildly incorrect tile counts. ### Final Answer Therefore, the correct answer is **2000**.