Question

Please answer my question soon

There is a narrow rectangular plot, reserved for a school, in Mumbai village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs.100 per metre it will cost the village panchayat Rs.75000 to fence the plot. What are the dimensions of the plot?
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Answer 1

★ Solution :-

In the following question, we are given with the ratio of the dimensions i.e, the measurements of length and breadth of a rectangular plot. We're also given with the total cost to fence and the rate to cost per metre to the plot. So,

First, we should find the perimeter of the rectangle. We can find the same by the values given about fencing.

Perimetre of the plot :-

According to the question,

$\sf \leadsto \dfrac{Total \: cost \: of \: fencing}{Cost \: of \: fencing \: per \: metre}$

$\sf \leadsto \dfrac{75000}{100}$

$\sf \leadsto 750$

Now, we can find the measurement of the length and breadth of the plot.

$\sf \leadsto {Perimetre}_{(Rectangle)} = 2 \: (Length + Breadth)$

$\sf \leadsto 750 = 2 \: (11x + 4x)$

$\sf \leadsto 750 = 2 \: (15x)$

$\sf \leadsto 750 = 30x$

$\sf \leadsto x = \dfrac{750}{30}$

$\sf \leadsto x = 25$

Length of the plot :

$\sf \leadsto 11x = 11(25)$

$\sf \leadsto 275 \: metres$

Breadth of the plot :

$\sf \leadsto 4x = 4(25)$

$\sf \leadsto 100 \: metres$

Therefore, the measurements of the dimensions of the plot are 275 and 100 metres respectively.