Final answer:
After solving the given equation for the breadth of the rectangular field and using it to find the perimeter, the total cost of fencing is calculated to be Rs. 960.
Step-by-step explanation:
The question is about finding the cost of fencing around a rectangular field, given that the field's length is three times its breadth and the area is 192m². Let the breadth be b meters, then the length will be 3b meters. According to the problem, the area of the rectangle is b × (3b) = 192. From this equation, we can find the value of b, and subsequently, the total length of the fence, which would be the perimeter of the rectangle.
To calculate the cost, we use the rate of Rs.15 per meter. After calculating the perimeter, we multiply it by this rate to find the total cost. Here's how the calculation is done:
- Area (A) = length × breadth = 3b² = 192m²
- Solve for b: b² = 192/3, b = √(64), b = 8m
- Length (L) = 3 × 8m = 24m
- Perimeter (P) = 2(L + B) = 2(24m + 8m) = 64m
- Cost of fencing = Perimeter × Cost per meter = 64m × Rs.15/m = Rs.960