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

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

Explanation:

Answer 2

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

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 =
`2x^2-16` and breadth =
`-x^2+4x+1`

Thus, perimeter of rectangle =
`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`

Thus, perimeter of rectangle is
`2x^2+8x-30` ........(1)

Perimeter of rectangle , when x = 3,

Put x= 3 in (1) ,

`2x^2+8x-30\Rightarrow 2(3)^2+8(3)-30 \Rightarrow 18+24-30=12`

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