Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are 2 x squared minus 16 feet and negative x squared plus 4 x plus 1 feet. Which expression represents the total perimeter of the table, and if x is equal to 3 , what is the length of the entire rubber bumper?
Answer
A
x squared plus 4 x minus 15 ; 3 feet
B
x squared plus 4 x minus 15 ; 6 feet
C
2 x squared plus 8 x minus 30 ; 12 feet
D
2 x squared plus 8 x minus 30 ; 6 feet
Explanation
The perimeter of a rectangle is 2(length + width). Adding the dimensions gives (2x² − 16) + (−x² + 4x + 1) = x² + 4x − 15, so the perimeter is 2x² + 8x − 30. When x = 3, this is 2(9) + 8(3) − 30 = 12 feet, matching choice C.
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