Question

find the perimeter of the rectangle. the perimeter is (simplify your answer.)

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is given by $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=2x^{2}+2x + 5$ and $w=x + 4$.

Step2: Substitute into formula

$P=2((2x^{2}+2x + 5)+(x + 4))$.

Step3: Simplify inside parentheses

First, simplify $(2x^{2}+2x + 5)+(x + 4)=2x^{2}+(2x+x)+(5 + 4)=2x^{2}+3x + 9$.

Step4: Multiply by 2

$P = 2(2x^{2}+3x + 9)=4x^{2}+6x+18$.

Answer:

$4x^{2}+6x + 18$