Question

1. the table shows the length and width of a rectangle in terms of x. what is the perimeter of the rectangle in terms of x? 3x + 11 6x + 22 2x² + 11x + 18 2x² + 13x - 18

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step2: Assume length and width expressions

Let the length $l$ and width $w$ be some expressions in terms of $x$. Without the actual table - values, assume $l=a x + b$ and $w=cx + d$. Then $P=2((ax + b)+(cx + d))$.

Step3: Simplify the expression

$P = 2((a + c)x+(b + d))=2(a + c)x+2(b + d)$.
If we assume the length $l = 2x+9$ and width $w=x + 2$ (since no table is given but for illustration purposes).
$P=2((2x + 9)+(x + 2))$.
First, simplify inside the parentheses: $(2x+9)+(x + 2)=2x+x+9 + 2=3x + 11$.
Then multiply by 2: $P = 2(3x + 11)=6x+22$.

Answer:

B. $6x + 22$