Answer
Each side is 21.21 inches
Work Step by Step
We know that each side of a square is equal and two sides of a square along with a diagonal form a right angled triangle. In the figure, we consider the triangle as ACD where $AD=CD=x$
We will use Pythagoras theorem to find out the length of the equal sides of the triangle. By Pythagoras theorem,
$P^2+B^2=H^2$
Where,
P= Perpendicular
B= Base
H= Hypotenuse
Here $P=B=x$ and $H=30$
Step-1 Substituting the formula:
$x^2+x^2=30^2$
$2x^2=900$
Step-2 Divide both sides by 2
$x^2=\frac{900}{2}$
$x^2=450$
Step-3 Using the square root property
$x=±\sqrt 450$
$x=±21.21
Since the side of a traingle cannot be negative, the length is approximately 21.21 inches.
Therefore, each side of the square is 21.21 inches.
