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

Let the length and breadth of the plot be 11x m and 4x m respectively.
Fencing all around = perimeter of the rectangular plot

Perimeter of the plot = \(\frac { 75000 }{ 100 }\) = 750 m

2(length + breadth) = 750

\(\Rightarrow\)2(11x + 4x) = 750

\(\Rightarrow\)2(15x) = 750

\(\Rightarrow\) 30x = 750

\(\Rightarrow\) x = 750 ÷ 30 = 25

Hence we have,

length =11x= 11 × 25 m = 275 m

and breadth = 4x=4 × 25 m = 100 m