question_answer

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?

Answer:

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

\[\therefore \] Perimeter of the plot = \[\frac{Total\text{ }cost}{Cost\text{ }of\text{ }1\text{ }meter}\]

\[=\frac{75000}{100}=750m\]

We know that perimeter of rectangle \[=\text{ }2\left( l+b \right)\]

\[\therefore \] According to question,

\[2\left( 11x+4x \right)=750\]

or, \[15x\text{ }=\frac{750}{2}\]

or, 15x = 375

or, \[x=\frac{375}{15}\]

or, x = 25

Hence, length of plot \[=11\times 25=275\]m

and breadth of the plot \[4\times 25=100\]m.