Question

(i) The cost of cultivating a rectangular field at Rs. 35 per square meter is Rs. 71400. If the width of the field is 40 m, find its length. Also, find the cost of cultivating at Rs. 50 per square meter.
(ii) The area of a rectangle is 540 square cm and its length is 36 cm. Find its width and perimeter.

Answer 1

Hint: We will first write down the formula for the area of a rectangle. Now, for (i), multiplying the area and cost, we will equate this all to 71400 by putting in the width of the field. Thus, we will get the length, and thus by find area, we can get the cost at Rs. 50. For (ii), we will just put in the given values in the formula for the area of the rectangle and get the width and then put in these values to get the perimeter.

Formula used:
We know that the area of a rectangle is given by $A = l \times b$ ………………..(1),
where $l$ is the length of the rectangle and $b$ is the breadth of the rectangle.

Complete step by step answer:
Part (i):
We see that the cost of cultivating the whole field at the rate of Rs. 35 per square meter. The cost is counted in the area of the field. So, this basically means that, if we multiply the area of field by $35$, we will get the cost which is given to be $Rs. 71400.$
So, we have $A \times 35 = 71400$.
Now, putting (1) in this, we will get
$ \Rightarrow l \times b \times 35 = 71400$
Taking the 35 from multiplication in LHS to division in RHS, we will get
$ \Rightarrow l \times b = \dfrac{{71400}}{{35}}{m^2}$
Simplifying the RHS, we will get
$ \Rightarrow l \times b = 2040{m^2}$
Since, we are already given that the breadth of the field is 40. So, we get
$ \Rightarrow l \times 40 = 2040{m^2}$
Taking the 40 from multiplication in LHS to division in RHS, we will get
$ \Rightarrow l = \dfrac{{2040}}{{40}}m$
Simplifying the RHS, we will get
$ \Rightarrow l = 51m$.
Now, let us find the area using (1). So, we get
$A = 51 \times 40 = 2040{m^2}$
Now, the cost of 1 square meter is = Rs. 50
So, cost of $2040$ square meter is = $Rs.50 \times 2040 = Rs.102000$.

Part (ii):
We are given that area of the rectangle is 540 square cm and the length is 36 cm.
Putting these values in (1), we will get
$ \Rightarrow 36 \times b = 540$
Taking the 36 from multiplication in LHS to division in RHS, we will get
$ \Rightarrow b = \dfrac{{540}}{{36}}cm$
Simplifying the RHS, we will get
$ \Rightarrow b = 15cm$.

Note:
The students must note that they should not forget to mention the units anywhere in the answer because just writing 41 does not represent anything but Rs. 41 represents money, 41 square meter/cm represents that we are talking about the area and 41 m or 41 cm represents we are talking about length.
Fun Fact: Every square is a rectangle but every rectangle is not a square. Basically, if the length and breadth of the rectangle are equal then we get a square.