The period [tex]T[/tex] (in seconds) of a pendulum is given by the formula:

[tex]T = 2 \pi \sqrt{\frac{L}{32}}[/tex]

where [tex]L[/tex] represents the length (in feet) of the pendulum. Given that [tex]\pi = 3.14[/tex] and the period is 1.57 seconds, what is the length of the pendulum?

A. 20 feet
B. 8 feet
C. 16 feet
D. 2 feet

To solve this problem, we need to find the length [tex]\( L \)[/tex] of a pendulum using the formula for the period [tex]\( T \)[/tex]:

[tex]\[ T = 2 \pi \sqrt{\frac{L}{32}} \][/tex]

Given:
- [tex]\( T = 1.57 \)[/tex] seconds
- [tex]\(\pi = 3.14\)[/tex]

Our goal is to find [tex]\( L \)[/tex].

### Step-by-Step Solution:

1. Rearrange the Formula:
Start with the formula for the period:
[tex]\[
T = 2 \pi \sqrt{\frac{L}{32}}
\][/tex]
To solve for [tex]\( \sqrt{\frac{L}{32}} \)[/tex], divide both sides by [tex]\( 2\pi \)[/tex]:
[tex]\[
\frac{T}{2\pi} = \sqrt{\frac{L}{32}}
\][/tex]

2. Square Both Sides:
Square both sides to eliminate the square root:
[tex]\[
\left(\frac{T}{2\pi}\right)^2 = \frac{L}{32}
\][/tex]

3. Solve for [tex]\( L \)[/tex]:
Multiply both sides by 32 to solve for [tex]\( L \)[/tex]:
[tex]\[
L = 32 \left(\frac{T}{2\pi}\right)^2
\][/tex]

4. Plug in the Values:
Substitute the given values [tex]\( T = 1.57 \)[/tex] and [tex]\(\pi = 3.14\)[/tex] into the equation:
[tex]\[
L = 32 \left(\frac{1.57}{2 \times 3.14}\right)^2
\][/tex]

5. Calculate:
Compute the term inside the parentheses:
[tex]\[
\frac{1.57}{6.28} \approx 0.25
\][/tex]

Then square it:
[tex]\[
(0.25)^2 = 0.0625
\][/tex]

Finally, multiply by 32:
[tex]\[
L = 32 \times 0.0625 = 2.0
\][/tex]

So, the length [tex]\( L \)[/tex] of the pendulum is [tex]\(\boxed{2}\)[/tex] feet.