Question

Field X and Y are to be enclosed with fencing at the cost of $Rs.40$ per meter. If the cost on field X is denoted by ${C_X}$ and that on field Y is denoted by ${C_Y}$ , we have

(A) ${C_X} = {C_Y}$
(B) ${C_X} < {C_Y}$
(C) ${C_X} > {C_Y}$
(D) Cannot be determined

Answer 1

Hint:
Start with finding the perimeter of both the fields. The perimeter is the sum of the length of each side of the field. The perimeter of the square is four times its side. Find the perimeter of X and Y separately and multiply it with the rate of fencing for finding the total cost of fencing ${C_X}$ and ${C_Y}$ . Now check for the relationship between these two.

Complete Step by Step Solution:
Here in this problem, we are given a diagram showing two fields X and Y with their dimensions. The cost of fencing these fields is $Rs.40$ per meter. The cost of field X and Y is given as ${C_X}$ and ${C_Y}$ . Now using this information we need to figure out which of the four given options is correct.
You must understand that the fencing will always be done exactly on the boundary of the field. Therefore, to find the total length of fencing required for both fields we must find out the perimeter of the fields. The perimeter of any two-dimensional polygon can be found by adding up the lengths of each side.

For field X, the total length of fencing $ = $ Sum of the lengths of all sides $ = $ Perimeter of X
$ \Rightarrow $ Perimeter of X $ = 470 + (180 + 290) + \left( {290 + 180} \right) + 470$
Now, these dimensions of sides of the field can be easily added as:
$ \Rightarrow $ Perimeter of X $ = 470 + 470 + 470 + 470 = 4 \times 470 = 1880{\text{m}}$
Similarly, for field Y, the total length of fencing $ = $ Sum of the lengths of all sides $ = $ Perimeter of Y
$ \Rightarrow $ Perimeter of Y $ = 470 + 470 + 470 + 470 = 4 \times 470 = 1880{\text{m}}$
For calculating the total cost of fencing be must multiply the perimeter with the rate off fencing, i.e. $Rs.40$ per meter
$ \Rightarrow $Cost of fencing X, i.e. ${C_X} = 1880 \times 40 = Rs.75200$
Similarly,
$ \Rightarrow $Cost of fencing Y, i.e. ${C_Y} = 1880 \times 40 = Rs.75200$
Therefore, we get ${C_X} = {C_Y}$

Hence, the option (A) is the correct answer.

Note:
In mensuration, the use of the fundamental concept of area and perimeter. An alternative approach to check for the relationship between ${C_X}$ and ${C_Y}$ can be taken by comparing the areas of the field X and Y. Since the rate of fencing is the same for both fields, the relation between the perimeter will be the same as the cost of fencing, i.e. ${C_X}$ and ${C_Y}$.