Question

A rectangular plot of land is 50m wide. The cost of fencing the plot at the rate of Rs.18 per meter is Rs.4680. Find
A. The length of the plot.
B. The cost of leveling the plot at the rate of Rs.7.6 per square meter.

Answer 1

Hint: Firstly we have to calculate the perimeter from the fencing cost. Then we have to assume the length and then calculate it from the perimeter. We have to remember the formulae of perimeter \[p=2\left( l+b \right)\]. After getting the length we have to calculate the area. Now if we multiply the rate of leveling cost we get the final answer.

Complete step-by-step answer:
Let us assume that the length of the plot is x meter.
In the question the width of the plot is given. Which is 50m.

Here is the diagram of that field.
We knew that fencing is done at the perimeter.
According to the question, the cost of fencing the plot at the rate of Rs.18 per meter is Rs.4680.
So the perimeter of the rectangular plot is,
\[\begin{align}
  & p=\dfrac{4680}{18} \\
 & \Rightarrow p=260 \\
\end{align}\]
The perimeter of the plot is 260m.
We know the width of the plot and we assume the length. By the formulae \[p=2\left( l+b \right)\] we can calculate the value of length.
Putting the value of “p” and “b” and evaluate further we get,
\[\begin{align}
  & 260=2\left( x+50 \right) \\
 & \Rightarrow \dfrac{260}{2}=x+50 \\
 & \Rightarrow x=130-50 \\
 & \Rightarrow x=80 \\
\end{align}\]

The length of the rectangular plot is 80m.
Now if we have to level the plot then we have to calculate the area of the plot first.
We know the area of a rectangular plot is \[a=l\times b\] where “l” is the length and “b” width of the plot.
Putting the value of “l” and “b” we get,
\[\begin{align}
  & a=80\times 50 \\
 & \Rightarrow a=4000 \\
\end{align}\]

So the area of the plot is 4000 square meter.
Now the rate of leveling the plot is Rs.7.6 per square meter. So leveling cost will be,
\[\begin{align}
  & 4000\times 7.6 \\
 & \Rightarrow 30400 \\
\end{align}\]

Now the length of the plot is 80m.
And the cost of leveling the plot is Rs.30400.

Note: We have to remember the formulae of perimeter \[p=2\left( l+b \right)\] where “l” is length and “b” width of the plot and area of the plot \[a=l\times b\]. Students get confused when to use the perimeter and when to use the area. We have to know that fencing is done at the perimeter, and leveling is done throughout the area.