# There is a narrow rectangular plot.The length and breadth of the plot are in the ratio of 11:4.At the rate of Rs.100 per meter it will cost village panchayat Rs.75000 to fence tge plot.What are the dimensions of the plot?

Length of the plot is 275 metres
Breadth of the plot is 100 metres

#### Explanation:

Let the length of the plot in metres be $l$
Let the breadth of the plot in metres be $b$
Given:
$l : b : : 11 : 4$
$\frac{l}{b} = \frac{11}{4}$
Cross multiplying
$4 l = 11 b$
$l = \frac{11}{4} b$
The perimeter of the plot is
$2 \left(\frac{11}{4} b + b\right)$
$= 2 \left(\frac{11}{4} b + \frac{4}{4} b\right)$
$= 2 \left(\frac{11}{4} + \frac{4}{4}\right) b$
$= 2 \left(\frac{11 + 4}{4}\right) b$
$= 2 \left(\frac{15}{4}\right) b$
$= \frac{2 \times 15}{4} b$
Length of perimeter in metres
$P = \frac{30}{4} b$
Cost of fencing per metre is
$C = 100$
Cost for fencing the plot A is
$A = P \times C = P \times 100 = 100 P$
Given:
Amount in rupees is
$A = 75000$

Equating the cost of fencing the plot to the amount
$100 P = 75000$
$P = \frac{75000}{100} = 750$
Perimeter in metres is
$P = 750$
$P = \left(\frac{30}{4}\right) b$
$\left(\frac{30}{4}\right) b = 750$
$b = 750 \times \left(\frac{4}{30}\right)$
Breadth of the plot in metres
$b = 100$
$L e n > h o f t h e p l o t \in m e t r e s$
$l = \left(\frac{11}{4}\right) b = \left(\frac{11}{4}\right) \times 100 = 275$
Length of the plot is 275 metres
Breadth of the plot is 100 metres