# 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

Updated on: 10-Oct-2022

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