Question : The sides of a triangular field are 120 m, 170 m and 250 m. The cost of levelling the field at the rate of INR 7.40/m2 is:
Option 1: INR 65,120
Option 2: INR 63,640
Option 3: INR 59,200
Option 4: INR 66,600
Correct Answer: INR 66,600
Solution :
Sides of triangular field = 120 m, 170 m, and 250 m.
Rate = Rs. 7.40/ m$^2$
Area of triangle = $\sqrt{S(S - a)(S - b)(S - c)}$
where semi-perimeter $S = \frac{a + b + c}{2}$, and $a,b,c$ are the sides of the triangle.
Dimensions of the triangular field are 120 m, 170 m and 250 m.
S = $\frac{120 + 170 + 250}{2}$= $\frac{540}{2}$ = 270 m
As we know,
Area of triangle = $\sqrt{S(S - a)(S - b)(S - c)}$
= $\sqrt{270(270 - 120)(270 - 170)(270 - 250)}$
= $\sqrt{270 \times 150 \times 100 \times 20}$
= $\sqrt{9 \times 3 \times 10 \times 5 \times 3 \times 10 \times 4 \times 5 \times 100}$
= 3 × 3 × 10 × 5 × 2 × 10
= 9000 m$^2$
Cost of levelling 1 m$^2$ = INR 7.40
Cost of levelling 9000 m$^2$ = 7.40 × 9000 = INR 66,600
So, the required cost of levelling is INR 66,600.
Hence, the correct answer is INR 66,600.
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