Question

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate of Rs. 100 per metre it will cost the village panchayat Rs. 75000 to fence the plot. What are the dimensions of the plot?
A. Length = 160m and Breadth = 80m
B. Length = 275m and Breadth = 100m
C. Length = 260m and Breadth = 120m
D. Length = 235m and Breadth = 90m

Answer 1

Hint: We will divide the total cost of the fencing by the rate per metre, which is 100, and get the perimeter of the plot. We know the perimeter of a rectangle is given by 2(l + b), so using this formula we can find the dimensions of the plot.

Complete step-by-step answer:

It is given in the question that Mahuli village has a rectangular plot that is reserved for the school. Also, the ratio of the length and breadth of the plot is given as 11:4, the rate of fencing per metre is Rs. 100 and the total amount paid by the village panchayat for fencing the entire plot is Rs. 75000. We have to find the dimensions of the plot. So, from the question, we get the ratio of the plot as,
$\dfrac{\text{Length}}{\text{Breadth}}=\dfrac{11}{4}$
Now, we will try to find the perimeter of the rectangle from the total cost of fencing paid by the panchayat. So, the total perimeter of the plot is given as,
$\dfrac{\text{Total cost of fencing}}{\text{Cost of 1m of fencing}}$
$\begin{align}
  & =\dfrac{75000}{100} \\
 & \Rightarrow 750m \\
\end{align}$
Thus, the perimeter of the plot for the school in the village is of 750m. We know that the perimeter of a rectangle is given by 2(l + b) and we have the perimeter of the rectangle as 750m. So,
2(l + b) = 750
But the length and breadth are in the ratio of 11:4, so equating them, we get,
$ \Rightarrow 2\left( 11x+4x \right)=750$
$ \Rightarrow 2\left( 15x \right)=750$
$ \Rightarrow 30x=750$
$ \Rightarrow x=\dfrac{750}{30}$
$ \Rightarrow x=25$
So, we get the length of the rectangular plot as $11\times 25=275m$. Similarly, we get the breadth as $4\times 25=100m$.

Therefore, we get the length of the rectangular plot as 275m and the breadth as 100m, so the correct answer is option B.

Note: In this type of questions, always use the derived formulas of polygons, like the perimeter of rectangle = 2(l + b), area of rectangle $=l\times b$, etc.

For example, if ABCD is a rectangle, then the perimeter of this rectangle is given as the length of its sides, which is (AB + BC + CD + DA) or (l + b + l + b) which is equal to 2(l + b). Thus, the perimeter of the rectangle is 2(l + b).