mrs. ishimitsu is installing a rubber bumper around the edge of her coffee table. the dimensions of the…
mrs. ishimitsu is installing a rubber bumper around the edge of her coffee table. the dimensions of the rectangular table are (2x² - 16) feet and (-x² + 4x + 1) feet. which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper?\no x² + 4x - 15; 3 feet\no x² + 4x - 15; 6 feet\no 2x² + 8x - 30; 6 feet\no 2x² + 8x - 30; 12 feet
Answer
Explanation:
Step1: Recall perimeter formula for rectangle
The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ and $w$ are the length and width. Here, $l=(2x^{2}-16)$ and $w=(-x^{2}+4x + 1)$.
Step2: First find $l + w$
[ \begin{align*} l + w&=(2x^{2}-16)+(-x^{2}+4x + 1)\ &=2x^{2}-16 - x^{2}+4x + 1\ &=(2x^{2}-x^{2})+4x+(1 - 16)\ &=x^{2}+4x - 15 \end{align*} ]
Step3: Then find the perimeter
$P = 2(l + w)=2(x^{2}+4x - 15)=2x^{2}+8x - 30$
Step4: Substitute $x = 3$ into the perimeter expression
[ \begin{align*} P&=2(3)^{2}+8(3)-30\ &=2\times9 + 24-30\ &=18+24 - 30\ &=12 \end{align*} ]
Answer:
$2x^{2}+8x - 30;12$ feet