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Liz just returned from a trip to visit some of the national parks with her family, and she wants to print her favorite picture from the trip to hang on her wall. She is not quite sure what size print she wants to get, although she does know that she wants the print to be square. She also wants to add a border that is 33 inches wide around the sides of the photo.\newlineThe total area of the photo and border in square inches can be modeled by the expression (x+6)(x+6)(x + 6)(x + 6), where xx is the width of the photo in inches. This expression can also be written in the form x2+12x+36x^2 + 12x + 36. What does the quantity 12x+3612x + 36 represent in the expression?\newlineChoices:\newline(A)the length of the photo and border together in inches\newline(B)the area of the photo in square inches\newline(C)the area of the border in square inches\newline(D)the perimeter around the outside of the border in inches

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Q. Liz just returned from a trip to visit some of the national parks with her family, and she wants to print her favorite picture from the trip to hang on her wall. She is not quite sure what size print she wants to get, although she does know that she wants the print to be square. She also wants to add a border that is 33 inches wide around the sides of the photo.\newlineThe total area of the photo and border in square inches can be modeled by the expression (x+6)(x+6)(x + 6)(x + 6), where xx is the width of the photo in inches. This expression can also be written in the form x2+12x+36x^2 + 12x + 36. What does the quantity 12x+3612x + 36 represent in the expression?\newlineChoices:\newline(A)the length of the photo and border together in inches\newline(B)the area of the photo in square inches\newline(C)the area of the 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 x+6)(x+6) whichisequivalentto$x2+12x+36x + 6)(x + 6)\, which is equivalent to \$x^2 + 12x + 36.
  2. Area of Photo: xx represents the width of the photo, so x2x^2 is the area of the photo itself.
  3. Area of Border Strips: The term 12x12x comes from expanding the expression (x+6)(x+6)(x + 6)(x + 6), where we get 2×6x2 \times 6x, which is the area of the four border strips that are xx inches by 33 inches.
  4. Area of Corner Squares: The constant 3636 comes from squaring the border width, which is 66 inches, so 6×66 \times 6 gives us the area of the four corner squares of the border.
  5. Total Border Area: Therefore, 12x12x represents the combined area of the four border strips, and 3636 represents the combined area of the four corner squares of the border.
  6. Total Border Area: Therefore, 12x12x represents the combined area of the four border strips, and 3636 represents the combined area of the four corner squares of the border.So, 12x+3612x + 36 represents the total area of the border around the photo.

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