To determine the perimeter [tex]\(P\)[/tex] of a rectangle, we need to use the perimeter formula for a rectangle, which is given by:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
In this particular problem, the length of the rectangle is provided as [tex]\(x+5\)[/tex] and the width is provided as [tex]\(y-1\)[/tex].
Step-by-step solution:
1. Identify the length and width:
- Length [tex]\( = x + 5 \)[/tex]
- Width [tex]\( = y - 1 \)[/tex]
2. Express the perimeter formula using the identified length and width:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
3. Substitute the values of length and width into the formula:
[tex]\[ P = 2 \times ((x + 5) + (y - 1)) \][/tex]
4. Simplify the expression inside the parentheses:
[tex]\[ P = 2 \times (x + y + 5 - 1) \][/tex]
5. Combine like terms inside the parentheses:
[tex]\[ P = 2 \times (x + y + 4) \][/tex]
6. Distribute the 2 across the terms inside the parentheses:
[tex]\[ P = 2 \times x + 2 \times y + 2 \times 4 \][/tex]
[tex]\[ P = 2x + 2y + 8 \][/tex]
Thus, the correct expression for the perimeter [tex]\(P\)[/tex] of the rectangle is:
[tex]\[ P = 2x + 2y + 8 \][/tex]
So, the answer is:
[tex]\[ P = 2 x + 2 y + 8 \][/tex]
Which matches the first option given:
[tex]\[ P = 2 x + 2 y + 8 \][/tex]
