Question

6. 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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Answer 1

Answer:

Cost = 75000

Rate = 100

Perimeter = Cost / Rate = 75000/100 = 750 m

Let sides be 11x and 4x .

Hence ,

2 ( 11x + 4x ) = 750

x = 25 .

Length = 11x = 11 * 25 = 275 m

Breadth = 4x = 4 * 25 = 100 m

Answer 2

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

∴ Perimeter of the plot = (Total Cost)/(Cost of 1 meter) = 75000/100 = 750 m

We know that Perimeter of rectangle = 2 (length + breadth)

Therefore, according to the question,

750 = 2(11x+4x)

⇒750 = 2×15x

⇒ 750 = 30x

⇒ 30x = 750

⇒x=750/30 = 25

Hence, length of rectangular plot = 11×25 = 275 m

And breadth of rectangular plot = 4×25= 100 m