Question

2. Write an expression for the perimeter of a rectangle with a length of(3x2 + x + 2) and a width of (-22 – 5x + 1).O 4248x 7.60 4224x + 34x28x + 6O 2x24x + 3

Answer 1

You have that the perimeter of the rectangle is given by the following formula:

$P=2l\text{ + 2w}$

l: length of the rectangle

w: width of the rectangle

$\begin{gathered} l=3x^2+x+2 \\ w=-x^2-5x+1 \end{gathered}$

Then, you replace the pevious expression for l and w in the formula for the perimeter, just as follow:

$\begin{gathered} P=2(3x^2+x+2)+2(-x^2-5x+1) \\ P=2(3x^2)+2(x)+2(2)+2(-x^2)+2(-5x)+2(1) \\ P=6x^2+2x+4-2x^2-10x+2 \\ P=4x^2-8x+6 \end{gathered}$

Hence, the perimeter of the rectangle is P = 4x2 - 8x + 6