Answer:
The exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]
Explanation:
Given the square in the attached image.
The length of the diagonal is;
[tex]d=28[/tex]
Let l represent the length of the sides;
[tex]\begin{gathered} l^2+l^2=28^2 \\ 2l^2=784 \\ l^2=\frac{784}{2} \\ l^2=392 \\ l=\sqrt[]{392} \\ l=14\sqrt[]{2} \end{gathered}[/tex]
The perimeter of a square can be calculated as;
[tex]\begin{gathered} P=4l \\ P=4(14\sqrt[]{2}) \\ P=56\sqrt[]{2} \end{gathered}[/tex]
Therefore, the exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]
