Question

If the area of a square field is $16$ hectares, then its perimeter is-
A.$1600m$
B.$160m$
C.$400m$
D.None of these

Answer 1

Hint: First convert hectares into square meters using formula$1$ hectare=$10,000$ square meters. Then use the formula of area of square which is given as- Area of square=${\left( {side} \right)^2}$ . Put the given values to find the length of each side. Then use the formula of perimeter of square which is given as-
$ \Rightarrow $ Perimeter of square=$4 \times $ length of each side
Put the value of length on each side and multiply to get the answer.

Complete step-by-step answer:
Given, the area of the square field is $16$ hectares.
We know that $1$ hectare=$10,000$ square meters
Then$16$ hectares=$160000$ square meters
We have to find its perimeter.
Let the length of each side of the square be a m.

Now we know that the formula of area of the square is –
Area of square=${\left( {side} \right)^2}$
Then on putting the given values, we get-
$ \Rightarrow 160000 = {a^2}$
On removing the square from the right side, we get-
$ \Rightarrow \sqrt {160000} = a$
We can write it as –
$ \Rightarrow a = \sqrt {16 \times 10 \times 10 \times 10 \times 10} $
On simplifying, we get-
$ \Rightarrow a = \sqrt {4 \times 4 \times 10 \times 10 \times 10 \times 10} $
On further simplifying we get-
$ \Rightarrow a = 4 \times 10 \times 10$
On multiplication, we get-
$ \Rightarrow a = 400m$
Now we know the formula of perimeter of square is given as-
$ \Rightarrow $ Perimeter of square=$4 \times $ length of each side
On putting the value of a in the formula we get-
$ \Rightarrow $ Perimeter of the square=$4 \times 400$
On multiplication, we get-
$ \Rightarrow $ Perimeter of the square=$1600m$
Hence the correct answer is option A.

Note: Here we can also add the obtained length of each side four times to get the perimeter. We know that perimeter is the sum of all sides of the given shape. So we can write-
$ \Rightarrow $ Perimeter of square =a +a+ a+ a
Now on putting the value, we get-
$ \Rightarrow $ Perimeter of square=$400 + 400 + 400 + 400$
On adding them, we get-
$ \Rightarrow $ Perimeter of the square=$1600m$