Question

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?

Answer 1

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