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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