How many tiles, each of area 400 `cm^(2)`, will be needed to pave a footpath which is 2 m wide and surrounds a grass plot 25 m long and 13 m wide ?

Answer

To solve the problem of how many tiles are needed to pave a footpath surrounding a grass plot, we can follow these steps:

### Step 1: Determine the dimensions of the grass plot.
- The grass plot has a length of 25 m and a width of 13 m.

### Step 2: Calculate the dimensions of the outer rectangle (including the footpath).
- The footpath is 2 m wide, which means we need to add 2 m to each side of the grass plot.
- **Length of the outer rectangle** = Length of grass plot + 2 m (left) + 2 m (right) = 25 m + 2 m + 2 m = 29 m.
- **Width of the outer rectangle** = Width of grass plot + 2 m (top) + 2 m (bottom) = 13 m + 2 m + 2 m = 17 m.

### Step 3: Calculate the area of the outer rectangle.
- Area of the outer rectangle = Length × Width = 29 m × 17 m = 493 m².

### Step 4: Calculate the area of the grass plot.
- Area of the grass plot = Length × Width = 25 m × 13 m = 325 m².

### Step 5: Calculate the area of the footpath.
- Area of the footpath = Area of the outer rectangle - Area of the grass plot = 493 m² - 325 m² = 168 m².

### Step 6: Convert the area of the footpath into square centimeters.
- Since 1 m² = 10,000 cm², we convert 168 m² to cm²:
- Area of footpath in cm² = 168 m² × 10,000 cm²/m² = 1,680,000 cm².

### Step 7: Determine the area of one tile.
- Each tile has an area of 400 cm².

### Step 8: Calculate the number of tiles required.
- Number of tiles required = Area of footpath / Area of one tile = 1,680,000 cm² / 400 cm² = 4200 tiles.

### Final Answer:
- **4200 tiles** are needed to pave the footpath.

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