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 m2 = 924 × 9.25 = INR 8,547 Hence, the correct answer is INR 8,547.
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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 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
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 internal length, breadth, and height of a cuboidal room are 12 m, 8 m, and 10 m, respectively. The total cost (in INR) of whitewashing only all four walls of the room at the cost of INR 25 per m2, is:
Option 1: 12,600
Option 2: 10,000
Option 3: 11,400
Option 4: 18,000
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