Area of a square is $ 169c{{m}^{2}} $ . Find its side.

Hint: We will directly use the formula, area of a square is equal to $ \left( sid{{e}^{2}} \right) $ . We will first assume the side of square as x cm, then we will get, area of square is equal to $ {{\left( xcm \right)}^{2}} $ , so we can write, $ 169={{\left( xcm \right)}^{2}} $ . We will solve this equation to get the value of x which will give us the value of the side of the square.

Complete step-by-step answer:
It is given in the question that we have to find the side of a square whose area is given as $ 169c{{m}^{2}} $ .
We know that a square is a polygon having 4 sides and all the sides are equal and are perpendicular to each other.
Now, let us assume that the side of the square is x cm. So, it can be represented diagrammatically as follows.

We know that the area of a square is given by, $ \left( sid{{e}^{2}} \right) $ . And we have been given the question that the area of a square is $ 169c{{m}^{2}} $ . So, we can write,
Area of square = $ \left( sid{{e}^{2}} \right)=169c{{m}^{2}} $
As we have already assumed the side of the square as z , we can write,
 $ {{\left( x \right)}^{2}}=169 $
On taking the square root on both the sides, we get,
 $ \begin{align}
  & x=\sqrt{169} \\
 & x=13 \\
\end{align} $
Thus, we get the value of x as 13cm.
Therefore, the side of the square whose area is $ 169c{{m}^{2}} $ is equal to 13 cm.
So, the correct answer is “Option A”.

Note: Majority of the students often get confused between the formula of area of square and perimeter of a square and as a result, they may write 4x = 169 and then solve further which will give them the wrong answer. So, the students must know that the perimeter of a square is given as $ 4\times side $ and the area of a square is given as $ \left( sid{{e}^{2}} \right) $ .