Question

The cost of fencing a rectangular field at Rs 18 per meter is Rs 1980. If the width of the field is 23 m. Find its length.

Answer 1

Hint Hint: First we will compute the total fenced by dividing the total cost of fencing with the cost of fencing a rectangular field. Then we will use the formula of perimeter of a rectangle,\[2\left( {l + b} \right)\], where \[l\] is the length and \[b\] is the breadth to find the length of the field.

Complete step-by-step answer:
We are given that the cost of fencing a rectangular field at Rs 18 per meter is Rs 1980 and the width of the field is 23 m.
Let us assume that the length is represented by \[l\] m.
First, we will compute the total fence by dividing the total cost of fencing with the cost of fencing a rectangular field.
\[
   \Rightarrow {\text{Total Fenced}} = \dfrac{{1980}}{{18}} \\
   \Rightarrow {\text{Total Fenced}} = 110{\text{ m}} \\
 \]
Since the fencing is done on the boundary of a rectangular field, the total fencing of a rectangular field is equal to the perimeter of a rectangle.
We know that the perimeter of a rectangle is calculated using the formula,\[2\left( {l + b} \right)\], where \[l\] is the length and \[b\] is the breadth.
Since we are given the width of a rectangle is 23 m, which is also the breadth of a rectangle.
Substituting the value of perimeter of a rectangle and breadth in the above formula of perimeter of a rectangle, we get
\[ \Rightarrow 110 = 2\left( {l + 23} \right)\]
Dividing the above equation by 2 on both sides, we get
\[
   \Rightarrow \dfrac{{110}}{2} = \dfrac{{2\left( {l + 23} \right)}}{2} \\
   \Rightarrow 55 = l + 23 \\
 \]
Subtracting the above equation by 23 on each side, we get
\[
   \Rightarrow 55 - 23 = l + 23 - 23 \\
   \Rightarrow 32 = l \\
   \Rightarrow l = 32{\text{ m}} \\
 \]
Thus, the length of a rectangular field is 32 m.

Note In solving these types of questions, students should remember that the perimeter of any shape is the sum of the length of all its sides. And there are four sides in a rectangle out of which opposite sides are equal and adjacent sides are different. And the adjacent sides of the rectangle are known as length and breadth. So students should know that the width is also a breadth. So, the formula will be the same as is given for the perimeter of a rectangular. One should also know that the fencing done on the boundary of a field is equal to the perimeter of any field. Students should also know that the total cost of fencing will be the product of cost of fencing per meter and the perimeter of the field.