Cost of leveling a triangular plot at 20 paise per m^2: Find the total cost to level a triangle with sides 72 m, 30 m, and 78 m.

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:Use Heron’s formula to compute the area from three sides, then multiply by the given rate (20 paise = Rs 0.20) to obtain cost. Given Data / Assumptions: Sides: 72 m, 30 m, 78 m. Rate: 20 paise per m^2 = Rs 0.20 per m^2. Concept / Approach:Heron’s formula: with semiperimeter s = (a + b + c)/2, area Δ = √[s(s − a)(s − b)(s − c)]. Cost = area * 0.20. Step-by-Step Solution: s = (72 + 30 + 78)/2 = 180/2 = 90.Δ = √[90 * (90 − 72) * (90 − 30) * (90 − 78)] = √(90 * 18 * 60 * 12).Compute: 90*18 = 1620; 60*12 = 720; product = 1,166,400; √ = 1080 m^2.Cost = 1080 * 0.20 = Rs 216. Verification / Alternative check:Right/acute check: sides satisfy triangle inequality; numerical square-root confirms an integer area 1080, making the rate multiplication exact. Why Other Options Are Wrong:Rs. 220, Rs. 200, Rs. 210, Rs. 224 differ from the exact multiplication of 1080 by Rs 0.20. Common Pitfalls:Treating 20 paise as Rs 20 or mixing units; or arithmetic mistakes in the product under the radical. Final Answer:Rs. 216

Cost of leveling a triangular plot at 20 paise per m^2: Find the total cost to level a triangle with sides 72 m, 30 m, and 78 m.

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