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geometry
A rectangular park has a 2 m wide footpath around its four sides. If the area of the outer rectangle is 285 square metres. If the park is 13 metres wide, find the coast of paving the footpath at the rate of Rs 5 per square metre.
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1 Reply
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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>
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