Question : The sides of a triangular park are 60 m, 112 m and 164 m. The cost of levelling the park at the rate of INR 8.50/m2 is:
Option 1: INR 18,164
Option 2: INR 17,085
Option 3: INR 17,136
Option 4: INR 18,316
Correct Answer: INR 17,136
Solution :
Given:
a = 60 m
b = 112 m
c = 164 m
Rate = INR 8.50/m
2
Now,
Semi perimeter, $(S) = \frac{60\ +\ 112\ +\ 164 }{2} =\ 168$
Area of the triangle
$A\ = \sqrt{168(168\ -\ 60)(168\ -\ 112)(168\ -\ 164)} $
$⇒A\ = \sqrt{168\ \times 108\ \times 56\ \times 4}$
$\therefore A\ = 2016$ m
2
So, the cost of levelling of 2016 m
2
of the park
$=\ 8.5\ \times 2016$
$=17136$
Hence, the correct answer is INR 17136.
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