A square field of area 31684 m2 is to be enclosed with the wireplaced at height 1 m, 2 m, 3 m, 4 m above the ground. What length of the wire will be required if its length required for each circuit is 5% greater than the perimeter of the field ?



A square field of area 31684 m2 is to be enclosed with the wireplaced at height 1 m, 2 m, 3 m, 4 m above the ground. What length of the wire will be required if its length required for each circuit is 5% greater than the perimeter of the field ?

A. 6456 m

B. 27666 m

C. 2990.4 m

D. 14

Answer : C. 2990.4 m


Explanation:


Given that a square field is to be enclosed by four wires at height 1m, 2m, 3m and 4m.


    Area of the square field = 31684 m2
    Let's find the perimeter of square

As we know


    Area of square = x2
    So,
    x2 = 31684 m2
    Taking square root on both sides
    √x2 = √31684 m2
    x = 178 m
    So, the length of one side of square is x = 178 m

As we know the perimeter of the square is calculated as


    P = 4x
    P = 4 * 178
    P = 712 m

Given that length of wire for each circuit is 5% more than the length of perimeter of square. So,


    Length of wire = Length of perimeter  + 5% of Length of perimeter  
    l = 712 + 0.05 * 712
    l = 712 + 35.6
    l = 747.6 m

As we need to enclose the square field by wires four times at different height; therefore,


    Total Length of wire = 4l
    Total Length of wire = 4 * 747.6
    Total Length of wire = 2990.4 m

So, total length of wire is 2990.4 m


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