Question

The formula for finding the area of a square is $A={{s}^{2}}$. How do you transform this formula to find a formula for the length of a side of a square with an area A?

Answer 1

Hint: Here, we are given the formula of the area of a square and using it we have to find the formula of the side of the square. The given formula is in terms of the side of the square. We shall try to modify the formula such that the formula transforms and is in terms of the area of the square.

Complete step by step solution:
In the given formula, we have to input the value of the side of the square to calculate the area of the square but the formula must be modified such that we shall input the area of the square to calculate the side of the square.
Given that $A={{s}^{2}}$
Where,
$A=$ area of the square
$s=$ side of the square
In order to replace the term square of side of square with only side of square, we shall find the square root of all the terms on the left-hand side and the right-hand side.
Square rooting both sides, we get
$\begin{align}
  & \Rightarrow \sqrt{A}=\sqrt{{{s}^{2}}} \\
 & \Rightarrow \sqrt{A}=\sqrt{s\times s} \\
\end{align}$
$\Rightarrow s=\sqrt{A}$
Therefore, the formula $A={{s}^{2}}$ is transformed into a formula for the length of a side of a square with an area A as $s=\sqrt{A}$.

Note:
The most fundamental quantity of a square is the length to the side of the square. Using the length of the side of a square, we can calculate its perimeter as well as its area. However, while performing big multiplication in such formulas, we must carefully multiply the correct numbers to avoid mistakes.