Question

Area of a square is given as $ 144\text{ c}{{\text{m}}^{2}} $ . What could be the side of the square?

Answer 1

Hint: We have given the area of a square i.e. $ 144\text{ c}{{\text{m}}^{2}} $ and are asked to find the side of the square. We know that the area of a square is equal to the square of the side. Let us assume that the side of a square is “a” then $ {{a}^{2}}=144 $ . Now, taking the square root on both the sides of this equation will give the value of “a” and hence we get the side of the square.

Complete step-by-step answer:
t is given that the area of the square is equal to $ 144\text{ c}{{\text{m}}^{2}} $ .
We know that square is made of 4 equal sides so let us assume that side of the square is “a”.
In the below figure, we have shown a square ABCD with one of its sides as “a”.
  

Now, we know that the area of a square is equal to the square of one of its sides which is shown by the below formula.
Area of a square ABCD $ ={{\left( side \right)}^{2}} $
As we have assumed that length of the side as “a” so substituting the value of side as “a” in the above equation we get,
Area of a square ABCD $ ={{\left( a \right)}^{2}} $
Substituting the value of area of a square as $ 144\text{ c}{{\text{m}}^{2}} $ in the above equation we get,
 $ 144c{{m}^{2}}={{a}^{2}} $
Taking square root on both the sides we get,
 $ \sqrt{144}cm=a $
We know that 144 is the perfect square of 12 so square roots of 144 is 12.
 $ 12cm=a $
From the above, we have calculated the side of the square as 12 cm.

Note: Two things should be kept in mind while solving the above problem is that:
First of all write the units of area and side of the square everywhere.
Second thing is to remember the square from 2 to 19. It will save your time in exams like if you know that 144 is the perfect square of 12 then you quickly get the side of the square. There are methods too to solve the square root of 3 or 4 or higher digits but remembering the perfect square till 19 will help you in competitive exams.