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.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Answer Key | Eligibility | Application | Selection Process | Result | Cutoff | Admit Card
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
