To find the perimeter [tex]\( P \)[/tex] of a rectangle, we use the formula:
[tex]\[ P = 2 \times (\text{Length} + \text{Width}) \][/tex]
Given:
- Length of the rectangle = [tex]\( x + 6 \)[/tex]
- Width of the rectangle = [tex]\( y - 1 \)[/tex]
Substitute the given length and width into the perimeter formula:
[tex]\[ P = 2 \times ((x + 6) + (y - 1)) \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ (x + 6) + (y - 1) = x + y + 6 - 1 \][/tex]
[tex]\[ = x + y + 5 \][/tex]
Now multiply by 2:
[tex]\[ P = 2 \times (x + y + 5) \][/tex]
[tex]\[ = 2x + 2y + 10 \][/tex]
Therefore, the perimeter [tex]\( P \)[/tex] of the rectangle is:
[tex]\[ P = 2x + 2y + 10 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{2x + 2y + 10} \][/tex]
