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?

1 Answer
Shiva Prakash M V
Jun 2, 2018

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
l/b=11/4
Cross multiplying
4l=11b
l=11/4b
The perimeter of the plot is
2(11/4b+b)
=2(11/4b+4/4b)
=2(11/4+4/4)b
=2((11+4)/4)b
=2(15/4)b
=(2xx15)/4b
Length of perimeter in metres
P=30/4b
Cost of fencing per metre is
C=100
Cost for fencing the plot A is
A=PxxC=Pxx100=100P
Given:
Amount in rupees is
A=75000

Equating the cost of fencing the plot to the amount
100P=75000
P=75000/100=750
Perimeter in metres is
P=750
P=(30/4)b
(30/4)b=750
b=750xx(4/30)
Breadth of the plot in metres
b=100
Length of the plot in metres
l=(11/4)b=(11/4)xx100=275
Length of the plot is 275 metres
Breadth of the plot is 100 metres

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