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 $(2x^{2}-16)$ feet and $(-x^{2}+4x + 1)$ feet. which expression represents the total perimeter of the table, and if $x = 3$, what is the length of the entire rubber bumper?\n$x^{2}+4x - 15$; 3 feet\n$x^{2}+4x - 15$; 6 feet\n$2x^{2}+8x - 30$; 6 feet\n$2x^{2}+8x - 30$; 12 feet

mrs. ishimitsu is installing a rubber bumper around the edge of her coffee table. the dimensions of the rectangular table are $(2x^{2}-16)$ feet and $(-x^{2}+4x + 1)$ feet. which expression represents the total perimeter of the table, and if $x = 3$, what is the length of the entire rubber bumper?\n$x^{2}+4x - 15$; 3 feet\n$x^{2}+4x - 15$; 6 feet\n$2x^{2}+8x - 30$; 6 feet\n$2x^{2}+8x - 30$; 12 feet

Answer

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

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}-16)) and (w=(-x^{2}+4x + 1)).

Step2: Substitute the values of (l) and (w) into the perimeter formula

[ \begin{align*} P&=2[(2x^{2}-16)+(-x^{2}+4x + 1)]\ &=2(2x^{2}-16 - x^{2}+4x + 1)\ &=2(x^{2}+4x-15)\ &=2x^{2}+8x - 30 \end{align*} ]

Step3: Substitute (x = 3) into the perimeter formula

When (x = 3), we have (P=2(3)^{2}+8(3)-30). First, calculate (2(3)^{2}=2\times9 = 18), (8(3)=24). Then (P=18 + 24-30=12).

Answer:

(2x^{2}+8x - 30;12) feet (the fourth option)