Given Data:
The length of the diagonal of the squre is:d=10 units.
Let 'a' be the length of a side of the given square.
The expression to caclculate the length of the side 'a' is,
[tex]\begin{gathered} d=\sqrt[]{a^2+a^2} \\ d=\sqrt[]{2a^2} \\ a=\sqrt[]{\frac{d^2}{2}} \end{gathered}[/tex]
Substitute values in the above expression.
[tex]\begin{gathered} a=\sqrt[]{\frac{10^2}{2}} \\ a=\sqrt[]{\frac{100}{2}} \\ a=\sqrt[]{50} \\ a=5\sqrt[]{2} \\ a=7.071\text{ units} \end{gathered}[/tex]
Thus, the length of the side a is 7.071 units.
