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?

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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?

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Answer 1 · 2018-06-02T16:27:32

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

Explanation:

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

Equating the cost of fencing the plot to the amount
$100 P = 75000$ $100P=75000$
$P = \frac{75000}{100} = 750$ $P=75000/100=750$
Perimeter in metres is
$P = 750$ $P=750$
$P = (\frac{30}{4}) b$ $P=(30/4)b$
$(\frac{30}{4}) b = 750$ $(30/4)b=750$
$b = 750 \times (\frac{4}{30})$ $b=750xx(4/30)$
Breadth of the plot in metres
$b = 100$ $b=100$
$L e n > h o f t h e p l o t \in m e t r e s$ $Length of the plot in metres$
$l = (\frac{11}{4}) b = (\frac{11}{4}) \times 100 = 275$ $l=(11/4)b=(11/4)xx100=275$
Length of the plot is 275 metres
Breadth of the plot is 100 metres

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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

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