Question : The sides of a triangular park are 35 m, 53 m, and 66 m. The cost of levelling the park at the rate of INR 9.25 per m2 is:
Option 1: INR 8,584
Option 2: INR 8,547
Option 3: INR 8,621
Option 4: INR 8,510
Correct Answer: INR 8,547
Solution : Given: The sides of a triangular park are 35 m, 53 m, and 66 m. The formulas used are, The area of the triangle using the Heron's formula = $\sqrt {s(s–a)(s–b)(s–c)}$, where the semi-perimetre($s$) = $\frac{a+b+c}{2}$ and $a,b,c$ are the sides of the triangle. ⇒ $s = \frac{35+53+66}{2}= \frac{154}{2}=77$ m The area of the triangle using the Heron's formula $=\sqrt {77(77–35)(77–53)(77–66)}$ $=\sqrt {77\times 7 \times 6\times 6\times 4\times 11}=11\times 7\times 6\times 2 = 924$ The cost of levelling the park at the rate of INR 9.25 per m 2 = 924 × 9.25 = INR 8,547 Hence, the correct answer is INR 8,547.
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