# A square field of area 31684 m^{2} 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 m^{2} 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 m ^{2}**

Let's find the perimeter of square

### As we know

**Area of square = x ^{2}**

So,

x

^{2}= 31684 m

^{2}

Taking square root on both sides

√x

^{2}= √31684 m

^{2}

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**