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Mitchell, a photographer, recently returned from a photo shoot in the Himalayas. Now in the editing phase, he decides that one photo of a climber needs an added visual effect. To give it the right look, he will place a solid border of equal width around the entire 2424-by-3636-inch photo. The total area of the photo and border in square inches can be modeled by the expression (24+2x)(36+2x)(24 + 2x)(36 + 2x), where xx is the width of the border in inches.\newlineWhat does the quantity 36+2x36 + 2x represent in the expression?\newline(A)the length of the photo and border together in inches\newline(B)the area of the border in square inches\newline(C)the total area of the photo and border in square inches\newline(D)the perimeter around the outside of the border in inches

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Q. Mitchell, a photographer, recently returned from a photo shoot in the Himalayas. Now in the editing phase, he decides that one photo of a climber needs an added visual effect. To give it the right look, he will place a solid border of equal width around the entire 2424-by-3636-inch photo. The total area of the photo and border in square inches can be modeled by the expression (24+2x)(36+2x)(24 + 2x)(36 + 2x), where xx is the width of the border in inches.\newlineWhat does the quantity 36+2x36 + 2x represent in the expression?\newline(A)the length of the photo and border together in inches\newline(B)the area of the border in square inches\newline(C)the total area of the photo and border in square inches\newline(D)the perimeter around the outside of the border in inches
  1. Total Area Expression: The expression for the total area is 24 + 2x)(36 + 2x)\. The first part, \$24 + 2x, represents the width of the photo plus the border on both sides. The second part, 36+2x36 + 2x, represents the length of the photo plus the border on both sides.
  2. Dimensions of the Photo: To find out what 36+2x36 + 2x represents, we need to look at the dimensions of the photo. The original photo is 2424 inches wide and 3636 inches long. The border is added around the photo, so it adds xx inches to each side of the photo.
  3. Adding Border to Length: Since the border is of equal width on all sides, we add xx inches to both the top and bottom of the photo's length. This means we add 2x2x inches to the original length of 3636 inches, giving us the expression 36+2x36 + 2x.
  4. Correct Choice Explanation: Therefore, 36+2x36 + 2x represents the total length of the photo including the border, not the area or the perimeter. So, the correct choice is (A) the length of the photo and border together in inches.

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