IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.

What is the perimeter, [tex][tex]$P$[/tex][/tex], of a rectangle that has a length of [tex]$x+5$[/tex] and a width of [tex]$y-1$[/tex]?

A. [tex]$P = 2x + 2y + 8$[/tex]
B. [tex][tex]$P = x + y + 4$[/tex][/tex]
C. [tex]$P = x + y + 6$[/tex]
D. [tex]$P = 2x + 2y - 8$[/tex]


Sagot :

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]