Given:
Square diagonal length = 12m
Find-:
The side length
Explanation-:
Let the side of a square is x
Triangle ABD is a right angle triangle
Use Pythagoras theorem is:
[tex]\text{ Base}^2+\text{ Perpendicular}^2=\text{ Hypotenuse}^2[/tex]
The hypotenuse is a diagonal
[tex]\begin{gathered} \text{ Base}=x \\ \\ \text{ Perpendicular}=x \\ \\ \text{ Hypotenuse}=12 \end{gathered}[/tex]
Apply theorem then,
[tex]\begin{gathered} x^2+x^2=12^2 \\ \\ x^2+x^2=144 \\ \\ 2x^2=144 \\ \\ x^2=\frac{144}{2} \\ \\ x^2=72 \\ \\ x=\sqrt{72} \\ \\ x=\sqrt{36\times2} \\ \\ x=\sqrt{6^2\times2} \\ \\ x=6\sqrt{2} \end{gathered}[/tex]
So the side length is 6√2 m
