Question

The cost of ploughing a square farm is the same as ploughing another farm that is rectangular in shape. The rate of ploughing is the same in both the cases. The side of the square farm is 20 m and the length of the rectangular farm is 40 m. Find the breadth of the rectangular farm?

Answer 1

Hint: We start solving the problem by drawing both square and rectangular farms with given information and also by assuming the breadth of the rectangular farm. We then use the fact that the cost for ploughing is laid for ploughing the total area of the farm. We then find the area of square farm and area of rectangular farm to equate them and get the required value of breadth of the rectangular farm.

Complete step-by-step answer:
According to the problem, we have a square field with a side 20 m and a rectangular field with length 40 m. We need to find the breadth of the rectangular farm if the cost of plough both square farm and rectangular form is the same. It is also given that the rate of ploughing is the same in both the cases.
Let us draw both the farms to get a better view.

We know that the cost of ploughing is laid for ploughing the total area of the field.
Let us assume the breadth of rectangular form be b m. We know that the cost of ploughing the area of the square = cost of ploughing the area of the rectangle.
We know that the area of the square with side a units is ${{a}^{2}}$ sq units. using this we find the area of the square farm.
Area of the square farm = $20\times 20{{m}^{2}}$.
Area of the square farm = $400{{m}^{2}}$ ---(1).
We know that the area of the rectangle length l and breadth b units is $l\times b$ sq units.
Area of the rectangular farm = $40\times b{{m}^{2}}$ ---(2).
From equations (1) and (2), we have
$\Rightarrow 40\times b=400$.
$\Rightarrow b=\dfrac{400}{40}$.
$\Rightarrow b=10m$.
We have found the breadth of the rectangular farm as 10 m.
The breadth of the rectangular farm is 10 m.

Note: Here we need to make sure that the rate of ploughing is the same for both the farms as it is the time required to plough $1{{m}^{2}}$ of area of farm. We should not make mistakes while calculating the areas and finding the breadth of the rectangular farm. We should confuse with the area of field. Similarly, we can expect problems by giving the triangular farms, parallelogram farms etc.