Question

Find the perimeter of the given rectangle.

x^2 + 3x - 1
2x^2 - 5

a. 6x^2 + 6x -12
b. 3x^2 - 2x - 1
c. 3x^2 + 3x - 6
d. 6x^2 - 4x - 2

Answer 1

To find the perimeter of a rectangle, we use the formula:

\[
P = 2(l + w)
\]

where \( l \) is the length and \( w \) is the width of the rectangle.

From the details you've provided, we have:

- Length \( l = x^2 + 3x - 1 \)
- Width \( w = 2x^2 - 5 \)

Now, we need to find \( l + w \):

\[
l + w = (x^2 + 3x - 1) + (2x^2 - 5)
\]

Combining like terms:

\[
l + w = x^2 + 2x^2 + 3x - 1 - 5
\]
\[
l + w = (1 + 2)x^2 + 3x + (-1 - 5)
\]
\[
l + w = 3x^2 + 3x - 6
\]

Now, we calculate the perimeter \( P \):

\[
P = 2(l + w) = 2(3x^2 + 3x - 6)
\]

Distributing the \( 2 \):

\[
P = 6x^2 + 6x - 12
\]

Thus, the perimeter of the rectangle is:

\[
\boxed{6x^2 + 6x - 12}
\]

So the correct answer is option (a) \( 6x^2 + 6x - 12 \).