Question

find the perimeter of the rectangle. (simplify your answer.) meters 9 meters 3x + 15 x + 8 x + 8 meters

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=\frac{3x + 15}{x + 8}$ and $w=\frac{9}{x + 8}$.

Step2: Substitute into formula

$P=2(\frac{3x + 15}{x + 8}+\frac{9}{x + 8})$.

Step3: Combine fractions

Since the denominators are the same, we have $P = 2\times\frac{3x+15 + 9}{x + 8}=2\times\frac{3x+24}{x + 8}$.

Step4: Factor and simplify

Factor out 3 from the numerator: $P = 2\times\frac{3(x + 8)}{x + 8}$. Then cancel out the $(x + 8)$ terms (assuming $x
eq - 8$), and we get $P=6$.

Answer:

$6$ meters