Question

The cost of fencing a rectangular field at 20 per metre is 2000. If the width of the field is 16 m find its length.

Answer 1

Hint:
With the given total cost we can find the perimeter of the field . We find the perimeter here because we are given fencing and fencing is done on the boundary and hence we get the perimeter to be 100 m and using the formula of perimeter of a rectangle , that is , $ \Rightarrow Perimeter = \left( {2l + 2b} \right)units$ we get the value of l.

Complete step by step solution:
We are given that total cost of fencing the rectangular field. Fencing is done on the boundary the length of fencing done is equal to the perimeter of the field. From the given total cost lets find the perimeter of the field. Since we are given that the cost of fencing 1 metre is 20
Then dividing the total cost by 20 gives us the perimeter.
$ \Rightarrow Perimeter = \dfrac{{2000}}{{20}} = 100m$
Hence we get the perimeter of the field to be 100 m. Now we are given that the width of the field is 16 m. So, let the length of the field be l m. We know that the perimeter of the rectangle is given by the formula
$ \Rightarrow Perimeter = \left( {2l + 2b} \right)units$
So lets substitute the values
$
   \Rightarrow 100 = \left( {2l + 2(16)} \right)m \\
   \Rightarrow 100 = 2l + 32 \\
   \Rightarrow 100 - 32 = 2l \\
   \Rightarrow 68 = 2l \\
   \Rightarrow l = \dfrac{{68}}{2} = 34m \\
 $

Hence we get the length of the field to be 34 m.

Note:
Many students get confused whether to find the area or perimeter.
Since the fence covers only the boundary it's enough to find the perimeter here and we need to find the area only when the inner part of the square is included.