There is a narrow rectangular plot, reserved for a school, in mahuli village. the length and breadth of the plot are in the ratio 11:4. At the rate rupees 100 per metre, it will cost the village panchayat rupees 75000 to fence the plot.what are the dimensions of the plot?

Given:

The length and breadth of the plot are in the ratio 11:4

At the rate rupees 100 per metre.

Tt will cost the village panchayat rupees 75000 to fence the plot.

To do:  Find the dimension of the plot

Solution: Ratio of Length and breadth =  $11 : 4$

Lets take the Length as  $11 x$  , and breadth as  $4 x$

Total cost of fencing  =  $75000$ ₹

cost per meter             =  $100 $₹

Total cost of fencing  =  Perimeter  $\times$  cost per meter 

75000   =  Perimeter  $\times$ 100

Rewrite,

 Perimeter   $\times$  100  =  75000

Perimeter  =  $\frac{75000} {100}$

Perimeter  =  750 m

Perimeter of Rectangle = $2 [length + breadth]$

$2 [length + breadth]  =  750$

$Length  +  breadth  =  \frac{750}{2}  =  375$

$11 x   +   4 x    =  375$

$15 x    =   375$

$ x      =   \frac{375}{15}$

  $x     =  25$

Length  =  $11 x  =  11  \times 25 =  275$ 

breadth  =  $4 x  =  4  \times 25 =  100$

Therefore the dimension of the plot is

Length  =  275 m  ,  Breadth  =  100 m

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Updated on: 10-Oct-2022

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