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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 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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Length=275 m and Breadth =100 m.

Length=322 m and Breadth =150 m.

Length=421 m and Breadth =143 m.

Length=115 m and Breadth =137 m.

answer is A.

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Detailed Solution

Given, total cost given is Rs. 75000.
Let the length and breadth of the plot be 11x m and 4x m respectively.
Fencing all around will be equal to perimeter of the rectangular plot.
Perimeter of rectangular plot will be,
Question Image

We know perimeter of rectangle is given by 2(length +breadth).
Substituting the values in above formula,

= 2 × 11 x + 4 x = 2 × 15 x = 30 x

Since perimeter of the rectangle is equal to perimeter of the rectangular plot.
Question Image

Substituting value of x in length and breadth.
Length is

= 11 × 25 m

= 275 m

And breadth is

= 4 × 25 m

= 100 m

The length and breadth of the plot are 275 m and 100 m respectively.
Correct option is 1.

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