Question

Find the area of the square, the length of whose diagonal is 25 cm.

Answer 1

Hint: We know that if the length of the side of the square is equal to x, then the length of diagonal is equal to \[x\sqrt{2}\]. Let us assume the side of square ABCD is equal to x. We know that the length of the diagonal of a square is equal to 25 cm. So, we will equal \[x\sqrt{2}\] to 25 cm, let us assume this equation as equation (1). Now we will find the value of x from equation (1). We know that if the length of the side of a square is equal to x, then the area of the square is equal to \[{{x}^{2}}\]. Now by using the concept, we can find the area of the required square.

Complete step-by-step answer:

Now let us assume a square ABCD whose length of diagonal is equal to 25 cm.
We know that if the length of the side of the square is equal to x, then the length of diagonal is equal to \[x\sqrt{2}\].
Let us assume the length of the square is equal to x.
From the diagram, it is clear that the length of diagonal of the square is equal to 25 cm.
\[\Rightarrow x\sqrt{2}=25\]
By using cross multiplication, we get
\[\Rightarrow x=\dfrac{25}{\sqrt{2}}.....(1)\]
We know that if the length of the side of a square is equal to x, then the area of the square is equal to \[{{x}^{2}}\].
Let us assume the area of the square is equal to A.
\[\Rightarrow A={{x}^{2}}......(2)\]
Now by substituting equation (!) in equation (2), we get
\[\begin{align}
  & \Rightarrow A={{\left( \dfrac{25}{\sqrt{2}} \right)}^{2}} \\
 & \Rightarrow A=\dfrac{625}{2} \\
 & \Rightarrow A=315.5......(3) \\
\end{align}\]
From equation (3), it is clear that the area of the square whose length of diagonal is 25 cm is equal to 315.5 sq.cm .

Note: Some students may have a misconception that if the length of the side of the square is equal to x, then the length of the diagonal is equal to \[\dfrac{x}{\sqrt{2}}\]. If this misconception is followed, the final answer may get interrupted. So, students should have a clear view about the concept.