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. \[\therefore \]\[Perimeter\text{ }of\text{ }the\text{ }plot\text{ }=\text{ }\frac{Total\text{ }cost}{Cost\text{ }of\text{ }1\text{ }meter}\]           \[=\frac{75000}{100}=750m\]                                                              We know that perimeter of rectangle = 2 (l + b) \[\therefore \] According to question,             \[2\left( 11x+4x \right)=750\] or,        \[15x=\frac{750}{2}\] or,         \[15x=375\]                                                                                                                                                         or,          \[x=\frac{375}{15}\] or,          x = 25 Hence, length of plot \[=11\times 25=275\text{ }m\] and breadth of the plot \[4\times 25=100\text{ }m.\]