Question

Which equation correctly represents the perimeter of the rectangle?
Responses


2(x+1)=2x+2


2(x+2)=2x+4


2(2x+3)=4x+3


2(2x + 3) = 4x + 6

Answer 1

To find the correct equation that represents the perimeter of a rectangle, we use the formula for the perimeter \( P \) of a rectangle, which is:

\[
P = 2(\text{length} + \text{width})
\]

Let's assume the length of the rectangle is represented by \( x + 1 \) and the width by \( x + 2 \). The perimeter would then be:

\[
P = 2((x + 1) + (x + 2)) = 2(2x + 3)
\]

Now, let's compare that with the options provided:

1. **\(2(x+1) = 2x + 2\)**: This is not the perimeter of the rectangle.
2. **\(2(x+2) = 2x + 4\)**: This is not the perimeter of the rectangle.
3. **\(2(2x + 3) = 4x + 3\)**: This is not correct because \( 2(2x + 3) = 4x + 6\).
4. **\(2(2x + 3) = 4x + 6\)**: This equation correctly represents the perimeter \( P = 2(2x + 3) \).

Thus, the correct equation that represents the perimeter of the rectangle is:

\[
2(2x + 3) = 4x + 6
\]