Connect with knowledgeable individuals and get your questions answered on IDNLearn.com. Get prompt and accurate answers to your questions from our experts who are always ready to help.
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]
[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]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.