Answer:
The length of each side of square is 6[tex]\sqrt{2}[/tex] inches
Step-by-step explanation:
Since the diagonal of square is 12 inches.
Let the side of the square in x inches.
As all the angles in square are right angles.
So Using the Pythagoras theorem , we can say that
[tex]x^{2} + x^{2} = 12^{2} \\[/tex]
⇒ [tex]2x^{2} = 144[/tex]
⇒ [tex]x^{2} = \frac{144}{2\\} } \\[/tex]
⇒ [tex]x^{2} = 72[/tex]
⇒[tex]x = \sqrt{72}[/tex]
⇒ [tex]x = \sqrt{36 }[/tex] ×[tex]\sqrt{2}[/tex]
⇒ x =[tex]6\sqrt{2}[/tex]
Hence the length of each side of square in radical form is [tex]6\sqrt{2}[/tex] inches
