Question

The sides of a rectangular field are in the ratio of 3:5 and its area is 2535 m2. Calculate the cost of fencing it at the rate of Rs.2.50/m.

• A. Rs.250
• B. Rs.260
• C. Rs.324
• D. Rs.423
• E. None of these

Answer 1

Answer: (E)

Step 1: Let the sides of the rectangular field be 3x and 5x.
Since the sides are in the ratio 3:5, we can assume the length of the field to be 5x meters and the width to be 3x meters. The area of the rectangle is given as 2535 m².

Step 2: Use the formula for area of a rectangle.
The area of a rectangle is given by:
Area = Length × Width.
Substituting the values:
2535 = 5x × 3x
2535 = 15x²

Step 3: Solve for x.
Divide both sides by 15:
x² = 2535 / 15
x² = 169
x = √169
x = 13

Step 4: Find the dimensions of the rectangle.
Now that we know x = 13, the dimensions of the field are:
Length = 5x = 5 × 13 = 65 meters
Width = 3x = 3 × 13 = 39 meters

Step 5: Find the perimeter of the rectangle.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × (Length + Width)
Perimeter = 2 × (65 + 39) = 2 × 104 = 208 meters.

Step 6: Calculate the cost of fencing.
The cost of fencing is given at the rate of Rs.2.50 per meter. Therefore, the total cost of fencing is:
Cost = Perimeter × Cost per meter
Cost = 208 × 2.50 = Rs. 520

Final Answer:
The cost of fencing the rectangular field is Rs. 520.

The correct option is (E): None of these.