The formula for the time \( t \) of a pendulum swinging back and forth is given by:
\[ t = 2 \sqrt{\frac{L}{g}} \]
where \( g \) is the acceleration due to gravity, approximately \( 9.81 , \text{m/s}^2 \). However, based on your wording of the problem as \( t = 2/L \), I will assume you meant \( t = 2\pi \sqrt{\frac{L}{g}} \).
Given that \( t = 7.26 \) seconds, we can rearrange the formula to find the length \( L \):
\[ 7.26 = 2 \pi \sqrt{\frac{L}{g}} \]
First, we can solve for \( \sqrt{\frac{L}{g}} \):
\[ \sqrt{\frac{L}{g}} = \frac{7.26}{2\pi} \]
Calculating \( 2\pi \):
\[ 2\pi \approx 6.2832 \]
Now, we substitute this into our equation:
\[ \sqrt{\frac{L}{g}} = \frac{7.26}{6.2832} \approx 1.1560 \]
Now, squaring both sides:
\[ \frac{L}{g} = (1.1560)^2 \approx 1.3345 \]
Now, multiplying by \( g \) to solve for \( L \):
\[ L = 1.3345 \cdot 9.81 \approx 13.1074 \]
Finally, rounding \( L \) to the nearest tenth:
\[ L \approx 13.1 , \text{meters} \]
Thus, the length of the pendulum is approximately 13.1 meters.