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

Related questions
Impact of this question
2584 views around the world
You can reuse this answer
Creative Commons License