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?\n○ x² + 4x - 15; 3 feet\n○ x² + 4x - 15; 6 feet\n○ 2x² + 8x - 30; 6 feet\n○ 2x² + 8x - 30; 12 feet

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?\n○ x² + 4x - 15; 3 feet\n○ x² + 4x - 15; 6 feet\n○ 2x² + 8x - 30; 6 feet\n○ 2x² + 8x - 30; 12 feet

Answer

Explanation:

Step1: Recall perimeter formula

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 $w=-x^{2}+4x + 1$. [P=2((2x^{2}-16)+(-x^{2}+4x + 1))]

Step2: Simplify the expression inside the parentheses

[ \begin{align*} (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*} ] So, $P = 2(x^{2}+4x - 15)=2x^{2}+8x - 30$.

Step3: Substitute $x = 3$

[ \begin{align*} P&=2(3)^{2}+8\times3 - 30\ &=2\times9+24 - 30\ &=18+24 - 30\ &=12 \end{align*} ]

Answer:

D. $2x^{2}+8x - 30;12$ feet