Question

The cost of fencing a square field at Rs. 14 per meter is Rs. 28000. Find the area of the field.

Answer 1

Hint: Assume the side of the square field to be $x$ \[m\] . We know that fencing is done along the perimeter and the perimeter of the square field is $4x$. Now, calculate the cost of the fencing of the square field. After calculation, we get Rs. $56x$ as the cost of the fencing of the square field. According to the question, it is given that the cost of the fencing is Rs. 28000. So, \[56x=28000\] . Now, solve this equation further and get the value of x. Now, we have got the value of x. We know the formula that the area of the square is \[{{(side)}^{2}}\] . Now, put the value of x in the formula and solve it further.

Complete step-by-step answer:

According to the question, it is given that we have a field that is in the shape of a square. The total cost of fencing that field is Rs. 28000 while the cost of fencing per meter is Rs. 28000.
The total cost of fencing = Rs. 28000 ………………….(1)
We know that fencing is always done along the boundary of the square field. In other words, we can say that the fencing is done along the perimeter of the field and this field has a square shape.
Let us assume the side of the square field is x meter.
We know that the perimeter of the square is the sum of its all sides.
Perimeter = \[x+x+x+x=4x\] meters.
Cost of fencing per meter = Rs. 14.
The total cost of fencing = Rs. 14(4x) …………………….(2)
From equation (1) and equation (2), we get
\[\begin{align}
  & 14(4x)=28000 \\
 & \Rightarrow x=\dfrac{28000}{56} \\
 & \Rightarrow x=500 \\
\end{align}\]
So, the side of the square is 500m.
We know the formula that the area of the square is \[{{(side)}^{2}}\] .
Now, putting the value of side in the formula, we get
\[Area={{(side)}^{2}}={{(500m)}^{2}}=250000{{m}^{2}}\] .
Hence, the area of the square field is 250000 \[{{m}^{2}}\] .

Note: In this question, one can think that fencing is done along the area. If we do so then we will get
\[14{{x}^{2}}=28000\]
\[\begin{align}
  & \Rightarrow {{x}^{2}}=2000 \\
 & \Rightarrow x=20\sqrt{5} \\
\end{align}\]
We will get \[20\sqrt{5}\] as the side of the square field which is wrong. Therefore, we have to keep in mind that fencing is done along the perimeter of the field.