Calculating Walkway Polishing Cost

First, find the area of a single rhombus slab.

• Diagonals: $d_1 = 50 \text{ cm} = 0.50 \text{ m}$, $d_2 = 35 \text{ cm} = 0.35 \text{ m}$
• Area of one slab = $\frac{1}{2} \times d_1 \times d_2$
• Area = $\frac{1}{2} \times 0.50 \text{ m} \times 0.35 \text{ m} = 0.0875 \text{ m}^2$

Next, calculate the total area of the walkway using all 2,500 slabs.

• Total Area = Number of slabs $\times$ Area of one slab
• Total Area = $2,500 \times 0.0875 \text{ m}^2 = 218.75 \text{ m}^2$

Then, calculate the total cost of polishing.

• Polishing Rate = ₹5 per m²
• Total Cost = Total Area $\times$ Rate
• Total Cost = $218.75 \text{ m}^2 \times ₹5/\text{m}^2 = ₹1093.75$

Finding Square Courtyard Side

Calculate the total area of the courtyard after adding the extra area.

• Total Courtyard Area = Walkway Area + Additional Area
• Total Courtyard Area = $218.75 \text{ m}^2 + 6.25 \text{ m}^2 = 225 \text{ m}^2$

Determine the side length of the square courtyard.

• Let the side length be 's'.
• Area of square = $s^2$
• $s^2 = 225 \text{ m}^2$
• $s = \sqrt{225 \text{ m}^2} = 15 \text{ m}$

The total cost of polishing is ₹1093.75, and the side of the square courtyard is 15 meters.