Explanation
We are given the following pendulum formula:
[tex]\begin{gathered} T=2\pi\sqrt{\frac{L}{32}} \\ where \\ T=timetaken \\ L=Length \end{gathered}[/tex]We are required to determine the length of the swing.
This is achieved thus:
[tex]\begin{gathered} T=2\pi\sqrt{\frac{L}{32}} \\ where \\ T=2.7seconds \\ \\ \therefore2.7=2\pi\sqrt{\frac{L}{32}} \\ \text{ Divide both sides by }2\pi \\ \frac{2.7}{2\pi}=\frac{2\pi\sqrt{\frac{L}{32}}}{2\pi} \\ \frac{2.7}{2\pi}=\sqrt{\frac{L}{32}} \\ \text{ Square both sides } \\ (\frac{2.7}{2\pi})^2=(\sqrt{\frac{L}{32}})^2 \\ (\frac{2.7}{2\pi})^2=\frac{L}{32} \\ \frac{L}{32}=\frac{2.7^2}{4\pi^2} \\ \\ \therefore L=\frac{2.7^2\times32}{4\pi^2} \\ L\approx5.9\text{ }feet \end{gathered}[/tex]Hence, the answer is:
[tex]L\approx5.9\text{ }feet[/tex]Option D is correct.