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Kylie enjoys arts and crafts. For her current project, she is making envelopes out of recycled paper. The dimensions will be the standard 66 inches by 99 inches. To give her envelopes a little flair, she will design a playful border, the same width all around, to line the edges of each. The area of the blank space inside the border in square inches can be modeled by the expression (6−2x)(9−2x)(6 - 2x)(9 - 2x), where xx is the width of the border in inches. What does the quantity 9−2x9 - 2x represent in the expression?\newline(A)the perimeter around the blank space inside the border in inches\newline(B)the length of the blank space inside the border in inches\newline(C)the area of the blank space inside the border in square inches\newline(D)the area of the border in square inches

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Q. Kylie enjoys arts and crafts. For her current project, she is making envelopes out of recycled paper. The dimensions will be the standard 66 inches by 99 inches. To give her envelopes a little flair, she will design a playful border, the same width all around, to line the edges of each. The area of the blank space inside the border in square inches can be modeled by the expression (6−2x)(9−2x)(6 - 2x)(9 - 2x), where xx is the width of the border in inches. What does the quantity 9−2x9 - 2x represent in the expression?\newline(A)the perimeter around the blank space inside the border in inches\newline(B)the length of the blank space inside the border in inches\newline(C)the area of the blank space inside the border in square inches\newline(D)the area of the border in square inches
  1. Area Expression Calculation: The expression for the area of the blank space is \(6 - 22x)(99 - 22x)\. We know that area is length times width.
  2. Width Calculation: The expression (6−2x)(6 - 2x) represents the width of the blank space after subtracting the border's width from both sides of the envelope's width.
  3. Length Calculation: Similarly, the expression (9−2x)(9 - 2x) represents the length of the blank space after subtracting the border's width from both sides of the envelope's length.
  4. Correct Choice Explanation: Since we're looking for what (9−2x)(9 - 2x) represents, and we've established it's related to the length after accounting for the border, the correct choice is (B) the length of the blank space inside the border in inches.

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