Question

If the area of a square is \[196{(cm)^2}\].Find the length of its diagonal.

Answer 1

Hint: To find the length of diagonal we need to find the length of the side first. We are given the area of the square. Using that we will find the side of the square.

Complete step-by-step answer:
Given that, the area of a square is \[196c{m^2}\].

We know that area of a square is given by
 \[area{\text{ }}of{\text{ }}a{\text{ }}square = side \times side\]
Putting the value of area
\[ \Rightarrow 196 = {(side)^2}\]
Taking square root on both sides
\[ \Rightarrow \sqrt {196} = side\]
\[ \Rightarrow side = 14cm\]
This side of the square is 14cm.
Now let’s find the diagonal of the square.
\[Diagonal{\text{ }}of{\text{ }}square = \sqrt 2 side\]
\[ \Rightarrow diagonal = \sqrt 2 \times 14\]cm
Hence the diagonal of the square is \[14\sqrt 2 cm\].
Note: In this problem where they have given area instead they can give perimeter and would ask to find diagonal. In that case also we will find the side first and then proceed to find the diagonal.
In some cases they will give diameter and would ask to find area and perimeter. At that time we will find the side of the square and proceed with it.