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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.

  

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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 ₹100 per metre it will cost the village panchayat ₹75000 to fence the plot. What are the dimensions of the plot?

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Let the length of the rectangular plot be 11x and breadth be 4x.

Rate of fencing per metre = ₹100

Total cost of fencing = ₹75000

Perimeter of the plot = 2(l + b)

= 2(11x + 4x) = 2 × 15x = 30x

Total amount of fencing = (30x × 100)

According to the question,

(30x × 100) = 75000

⇒ 3000x = 75000

⇒ x = \(\frac{75000}{3000}\)

⇒ x = 25

Length of the plot = 11x

= 11 × 25 = 275m

Breadth of the plot = 4 × 25

= 100 m.

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