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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

Respuesta :

Answer:

[tex]2x^2+8x-30[/tex] represents the total perimeter of the table, and if x = 3 the lentgh of entire rubber bumper is 12 feet.

Step-by-step explanation:

Perimeter is defined as the sum of sides.

For a rectangle having dimension length 'L' and breadth 'B' Since, rectangle has two sides equal.

Perimeter of rectangle = 2 ( length + breadth )

Here, given rectangle has dimension

Length = [tex]2x^2-16[/tex] and breadth = [tex]-x^2+4x+1[/tex]

Thus, perimeter of rectangle = [tex]2(2x^2-16+(-x^2+4x+1))[/tex]

                                              [tex]=2(2x^2-16-x^2+4x+1)[/tex]

                                               [tex]=2(x^2+4x-15)[/tex]

                                                [tex]=2x^2+8x-30[/tex]

Thus, perimeter of rectangle is [tex]2x^2+8x-30[/tex]   ........(1)

Perimeter of rectangle , when x = 3,

Put x= 3 in (1) ,

[tex]2x^2+8x-30\Rightarrow 2(3)^2+8(3)-30 \Rightarrow 18+24-30=12[/tex]

Thus, [tex]2x^2+8x-30[/tex] represents the total perimeter of the table, and if x = 3 the lentgh of entire rubber bumper is 12 feet.

Answer:

The Answer is D 2x2 + 8x – 30; 12 feet

Step-by-step explanation:

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