Question

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?

x2 + 4x – 15; 3 feet
x2 + 4x – 15; 6 feet
2x2 + 8x – 30; 6 feet
2x2 + 8x – 30; 12 feet

Answer 1

Answer:

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

Step-by-step explanation:

Given:- Table is rectangular

length of table = $2x^{2} -16$ feet

breadth of table = $-x^{2} +4x+1$ feet

Formula used:- Perimeter of rectangle= 2×(length+breadth)

Total perimeter of table=2×($(2x^{2} -16)+(-x^{2} +4x+1)$)

                                      =2×($2x^{2} -16-x^{2} +4x+1$)

                                      =2×($x^{2} +4x-15$)

                                      =$2x^{2} +8x-30$

Length of Entire rubber when x=3, is = $2(3^{2})+8(3)-30$

                                                             =(2×9)+24-30

                                                             =18+24-30

                                                             =42-30

                                                             =12 feet