Question

The cost of cultivating a rectangular field at the rate of rupees $5$ per square metre is rupees $2880$. If the length of the field is $32$ m, find the cost of fencing the field at the rate of rupees $11.25$per metre.

Answer 1

Step 1. Finding the area of the rectangular field:

Given, rupees $5$ is needed for area $=1$ square metre

Then rupees $1$ is needed for area $=\frac{1}{5}$ square metre.

Then rupees $2880$ is needed for area $=\frac{1}{5}\times 2880$

$=576$square metre

So, the area of the rectangular field is $576$ square metre.

Step 2. Finding the breadth of the rectangular field:

Let the length of the rectangular field is $l$ and the breadth is $b$.

Given the length of the rectangular field, $l=32$ m

We know, the area of the rectangle $=length\times breadth=l\times b$

We find the area of the rectangular field $=576$square metre

$l\times b=576$

$32\times b=576$

$b=\frac{576}{32}=18$m

So, we got the breadth of the rectangular field $18$m.

Step 3. Finding the perimeter of the rectangular field:

We know the perimeter of a rectangle $=2\left(length\times breadth\right)$

So, the perimeter of the rectangular field $=2\times \left(32+18\right)$

$2\times 50=100$m

So, the perimeter of the rectangular field is $100$ m.

Step 4. Find the cost of fencing:

Given, cost of fencing of $1$ metre $=11.25$

cost of fencing of $100$metre $=100\times 11.25=1125$Rupees

Hence, the cost of fencing the rectangular field is $1125$ Rupees.