To solve for [tex]\( c \)[/tex] in the given formula for the perimeter [tex]\( P \)[/tex] of a parallelogram with sides [tex]\( b \)[/tex] and [tex]\( c \)[/tex], we start with the equation:
[tex]\[ P = 2b + 2c \][/tex]
### Step-by-Step Solution:
1. Isolate the term involving [tex]\( c \)[/tex]:
[tex]\[
P = 2b + 2c
\][/tex]
Subtract [tex]\( 2b \)[/tex] from both sides:
[tex]\[
P - 2b = 2c
\][/tex]
2. Solve for [tex]\( c \)[/tex]:
Divide both sides by 2:
[tex]\[
c = \frac{P - 2b}{2}
\][/tex]
3. Express the equation in a simpler form:
The equation [tex]\( c = \frac{P - 2b}{2} \)[/tex] can also be written as:
[tex]\[
c = \frac{P}{2} - b
\][/tex]
### Matching with Given Choices:
Now match this derived equation [tex]\( c = \frac{P}{2} - b \)[/tex] with the given choices:
- A. [tex]\( c = \frac{P}{4b} \)[/tex]
- B. [tex]\( c = \frac{P}{2} - b \)[/tex]
- C. [tex]\( c = \frac{P}{2} + b \)[/tex]
- D. [tex]\( c = \frac{\rho}{2} - \frac{b}{2} \)[/tex]
From the options, we see that the matching choice is:
- B. [tex]\( c = \frac{P}{2} - b \)[/tex]
So the correct answer is:
[tex]\[ \boxed{B} \][/tex]
