Question

A rectangular field of length 242 m has an area of 4840 m2. What will be the cost of fencing if the cost of fencing required to cover all the four sides, if one metre of fencing costs 5 paise.

Answer 1

Hint: Find Perimeter and multiply it with the cost of fencing per meter.
To find the total cost, we need the perimeter of the rectangular field but we are not given the measurement of breadth. So, we need to find that, since in the question we are given the area, we use that and find breadth and the following with calculating the perimeter and in the end, obtaining the cost of fencing.

Complete step by step solution:
 We are given the following
Length = $242m$
Area = $4840{m^2}$
Cost of fencing per meter = $5paise$
The formula that shall be used in this problem
Area of the rectangular field = (length × breadth)
Perimeter of the rectangular field = 2 × (length + breadth)
Total cost of fencing of the rectangular field = (Perimeter × cost of fencing per meter)

So, we begin by finding the breadth.

Since, we are given the area, with which we can find the breadth.

Area of the rectangular field = (length × breadth)

\[
   \Rightarrow {\text{ }}4840{\text{ }} = {\text{ }}\left( {242\; \times {\text{ }}breadth} \right) \\
  breadth{\text{ }} = {\text{ }}20{\text{ }}m \\
 \]

Now, that we have breadth of the rectangular field, we can proceed to calculate the perimeter of the rectangular field by,

Perimeter of the rectangular field = 2 × (length + breadth)

\[\begin{array}{*{20}{l}}
  { \Rightarrow {\text{ }}2\; \times {\text{ }}\left( {242{\text{ }} + {\text{ }}20} \right)} \\
  { \Rightarrow {\text{ }}524{\text{ }}m}
\end{array}\]

Now, we have obtained the perimeter as well. The next and final step is finding the cost of fencing.

Total cost of fencing of the rectangular field = (Perimeter × cost of fencing per meter)

\[\begin{array}{*{20}{l}}
  { \Rightarrow {\text{ }}\left( {524\; \times {\text{ }}0.05} \right)} \\
  { \Rightarrow {\text{ 26}}{\text{.2}}}
\end{array}\]

This is the cost of fencing the whole rectangular field on all the four sides.

Note: While calculating the cost and when converting paise into rupees, we need to make sure the decimal is correct such that a wrong answer is avoided and as long as the cost per meter is in rupees, then there is no need of conversion.