To find the cost of paving the footpath, we need to determine the area of the footpath and then multiply it by the cost per square meter.<div>
</div><div>Let’s assume the length of the park (excluding the footpath) is L meters. The width of the park (excluding the footpath) is given as 13 meters.</div><div>
</div><div>The length of the outer rectangle, including the footpath, would be L + 4 meters (2 meters for each side of the footpath).</div><div>
</div><div>The width of the outer rectangle, including the footpath, would be 13 + 4 meters (2 meters for each side of the footpath).</div><div>
</div><div>The area of the outer rectangle can be calculated by multiplying its length and width:</div><div>
</div><div>Area of the outer rectangle = (L + 4) * (13 + 4)</div><div>
</div><div>We are given that the area of the outer rectangle is 285 square meters, so we can write:</div><div>
</div><div>(L + 4) * (13 + 4) = 285</div><div>
</div><div>Expanding this equation, we have:</div><div>
</div><div>L * 13 + L * 4 + 4 * 13 + 4 * 4 = 285</div><div>
</div><div>13L + 4L + 52 + 16 = 285</div><div>
</div><div>17L + 68 = 285</div><div>
</div><div>17L = 285 – 68</div><div>
</div><div>17L = 217</div><div>
</div><div>L = 217 / 17</div><div>
</div><div>L = 12.7647 meters (approximately)</div><div>
</div><div>Now that we know the length of the park (excluding the footpath), we can calculate the area of the footpath:</div><div>
</div><div>Area of the footpath = (L + 4) * (13 + 4) – L * 13</div><div>
</div><div>Area of the footpath = (12.7647 + 4) * (13 + 4) – 12.7647 * 13</div><div>
</div><div>Area of the footpath = 16.7647 * 17 – 165.9411</div><div>
</div><div>Area of the footpath ≈ 283.3529 square meters</div><div>
</div><div>Finally, we can calculate the cost of paving the footpath by multiplying the area of the footpath by the cost per square meter:</div><div>
</div><div>Cost of paving the footpath = Area of the footpath * Cost per square meter</div><div>
</div><div>Cost of paving the footpath = 283.3529 * 5</div><div>
</div><div>Cost of paving the footpath ≈ Rs 1416.76</div><div>
</div><div>Therefore, the cost of paving the footpath at the rate of Rs 5 per square meter would be approximately Rs 1416.76.</div>