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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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
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
Question : The internal length of a room is two times its breadth and three times its height. The total cost of painting its four walls at the rate of INR 25/m2 is INR 3,600. What is the cost of laying a carpet on its floor at the rate of INR 90.50/m2?
Option 1: INR 6,516
Option 2: INR 7,240
Option 3: INR 5,430
Option 4: INR 5,970
Question : A field is in the form of a circle. The cost of fencing around it at INR 12 per metre is INR 2,640. What is the area (in m2) of the field? (Take $\pi=\frac{22}{7}$)
Option 1: 1,925 m2
Option 2: 3,850 m2
Option 3: 2,772 m2
Option 4: 5,544 m2
Question : The diagonal of a quadrilateral-shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. The area of the field is:
Option 1: 252 m2
Option 2: 156 m2
Option 3: 96 m2
Option 4: 1152 m2
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