Question

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio of $11:4$ At the rate of $₹100permeter$ it will cost the village panchayat $₹75000$to fence the plot. What are the dimensions of the plot?

Answer 1

Step-1: Given Information

The length and breadth of the plot are in the ratio of $11:4$

Let the length of the rectangular plot be $11x$

Let the breadth of the rectangular plot be $4x$

Rate of fencing per meter = $₹100$

The total cost of fencing = $₹75000$

Step-2: Find the length or fencing or perimeter of the rectangular plot

$Perimeteroftheplot=2\times (l+b)$

$Perimeteroftheplot=2\times (11x+4x)$

$Perimeteroftheplot=2\times \left(15x\right)$

$Perimeteroftheplot=30xm$

Step-3: Find the value of $x$

Cost of fencing one meter = $₹100$

Cost of fencing of $30xm=30x\times 100=3000x$

and, The total cost of fencing = $₹75000$

According to the given details, the equation becomes

$3000x=75000$

$x=\frac{75000}{3000}$

$x=25m$

Step-4: Find the dimensions of the plot

Length of the plot$=11x=11\times 25=275m$

The breadth of the plot $=4\times 25=100m$

Hence, the Length of the plot $=275m$ and the Breadth of the plot $=100m$