We are given that the perimeter of a square is 68. Since the perimeter of a figure is the sum of all of its sides then the formula for the perimeter of a square is:
[tex]P=4l[/tex]Where "l" is the length of its sides. We can solve for "l" by dividing both sides by 4:
[tex]\frac{P}{4}=l[/tex]Replacing the value of the perimeter:
[tex]\begin{gathered} \frac{68}{4}=l \\ 17=l \end{gathered}[/tex]Now, the length of the diagonal of a square is:
[tex]d=\sqrt[]{2}l[/tex]Replacing the value of "l":
[tex]d=(\sqrt[]{2})(17)[/tex]Solving the operations:
[tex]d=24.0[/tex]Therefore, the length of the diagonal is 24 feet.
