Question

A rectangular field has its length and breadth in the ratio 5 : 3. Its area is 3.75 hectares. Find the cost of the fencing if it is at Rs. 5 per meter.
$\left( A \right)$ Rs. 400
$\left( B \right)$ Rs. 4000
$\left( C \right)$ Rs. 1000
$\left( D \right)$ Rs. 18,000

Answer 1

Hint – In this question assume any different variables be the length and the breadth of the rectangular field and calculate length in terms of breadth or vice versa as ratio is given and use the concept that area of the rectangular field is length times breadth so use these concepts to reach the solution of the question.

Complete step-by-step answer:

Given data:
Ratio of length and breadth of the rectangular field is (5:3)............. (1)
Its area (A) is = 3.75 hectares................... (2)
Now let the length of the rectangular field be x meter and breadth of the rectangular field is y meter.
So from equation (1) we have,
$ \Rightarrow \dfrac{x}{y} = \dfrac{5}{3}$
$ \Rightarrow x = \dfrac{5}{3}y$.................. (3)
Now as we know that the area of the rectangle is the product of the length and the breadth of the rectangle.
So the area of the rectangle is
$ \Rightarrow A = xy$Square meter.
Now from equation (3) we have,
$ \Rightarrow A = \dfrac{5}{3}y\left( y \right) = \dfrac{5}{3}{y^2}$Square meter.
Now from equation (2) we have,
$ \Rightarrow $A = 3.75 hectare$ = \dfrac{5}{3}{y^2}$Square meter................ (4)
Now as we know that 1 hectare = 10000 square meter.......... (5)
Therefore from equation (4) and (5) we have,
$ \Rightarrow $A = 3.75 $ \times $ 10000 square meter$ = \dfrac{5}{3}{y^2}$Square meter
Now simplify this equation we have,
$ \Rightarrow 37500 = \dfrac{5}{3}{y^2}$
Now calculate the value of y (i.e. breadth) we have
$ \Rightarrow y = \sqrt {\dfrac{{37500\left( 3 \right)}}{5}} = \sqrt {22500} = 150$ Meter.
Now from equation (3) we have,
$ \Rightarrow x = \dfrac{5}{3}\left( {150} \right) = 250$ Meter.
Now the cost of fencing is the perimeter of the rectangle.
As we know that the perimeter of any shape is the sum of all the side lengths of the shape.
So the perimeter of the rectangular field = 2(x + y)
Now substitute the values we have,
So the perimeter or the fencing required for the rectangular field = 2(250 + 150) = 2(400) = 800 meter.
Now it is given that the cost of fencing is at Rs. 5 per meter.
So the cost of 800 m fencing is = 800(5) = Rs. 4000
So this is the required answer.
Note – Whenever we face such types of questions the key concept we have to remember is that always recall that the perimeter of any shape is the sum of all the side lengths of the shape, so find out the length and breadth of the rectangular field then substitute these values in the formula of the perimeter as above and simplify we will get the required answer.