To find the total cost of fencing the rectangular field, we first need to determine its perimeter. We are given the length and the area of the field.
Field Dimensions Calculation
The area (\(A\)) of a rectangle is calculated by multiplying its length (\(L\)) and width (\(W\)). We have:
- \(L = 200 \, \text{m}\)
- \(A = 3000 \, \text{m}^2\)
Using the area formula \(A = L \times W\), we can find the width:
\(W = \frac{A}{L} = \frac{3000 \, \text{m}^2}{200 \, \text{m}} = 15 \, \text{m}\)
Field Perimeter Calculation
The perimeter (\(P\)) of a rectangle is calculated using the formula \(P = 2 \times (L + W)\). Now that we know the length and width:
- \(L = 200 \, \text{m}\)
- \(W = 15 \, \text{m}\)
Calculate the perimeter:
\(P = 2 \times (200 \, \text{m} + 15 \, \text{m}) = 2 \times (215 \, \text{m}) = 430 \, \text{m}\)
Total Fencing Cost Calculation
The cost of fencing is given as 5 rupees per metre. To find the total cost, multiply the perimeter by the cost per metre:
- Perimeter (\(P\)) = 430 m
- Cost per metre = 5 rupees/m
Total Cost = \(P \times \text{Cost per metre}\)
\(\text{Total Cost} = 430 \, \text{m} \times 5 \, \text{rupees/m} = 2150 \, \text{rupees}\)
Therefore, the total cost of fencing the field is 2150 rupees.
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Important Questions from 2-D Mensuration
- The length of a rectangular plot is $(x^2 + xy + y^2)$ m and its breadth is $(x^2 - 5xy - y^2)$ m.
Find its perimeter, when $x = 1$ and $y = -1$. - The ratio between the perimeter and breadth of a rectangle is 3: 1. If the area of the rectangle is $98 \text{ cm}^2$, find the perimeter (in cm) of the rectangle.
The shorter side of a rectangle is 15 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$) - Find the circumference (in m) of the largest circle that can be inscribed in a rectangle whose dimensions are given as 114 m and 63 m.
Take $\pi = \frac{22}{7}$
