Step 1: draw the diagram
The perimeter of a square is 4L
[tex]\begin{gathered} \text{peremeter}=4L \\ 48=4l \\ l=\frac{48}{4} \\ l=12 \end{gathered}[/tex]
The diagonal of the square is hypotenuse side represented by D
Using Pythagoras theorem, we have
[tex]\begin{gathered} \text{hyp}^2=\text{opp}^2+\text{adj}^2 \\ D^2=L^2+L^2 \end{gathered}[/tex][tex]\begin{gathered} D^2=12^2+12^2 \\ =144+144 \\ =288 \\ D=\sqrt[\square]{288} \\ D=16.97 \end{gathered}[/tex]
Hence the approximate length of the diagonal is 17ft
