isabella292008
Answered

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What is the perimeter, [tex]\( P \)[/tex], of a rectangle that has a length of [tex]\( x+6 \)[/tex] and a width of [tex]\( y-1 \)[/tex]?

A. [tex]\( P = x + y + 5 \)[/tex]
B. [tex]\( P = x + y - 7 \)[/tex]
C. [tex]\( P = 2x + 2y + 10 \)[/tex]
D. [tex]\( P = 2x + 2y - 10 \)[/tex]

Sagot :

GinnyAnswer
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]
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