Addison, a carpenter, is installing a new set of closet doors with a simple moulding for a client's bedroom. The closet doors are $75$ inches wide and $85$ inches tall, and the moulding will be an equal width around the sides and top of the doors. The total area of the closet doors and moulding in square inches can be modeled by the expression $(75 + 2x)(85 + x)$ , where $x$ is the width of the moulding in inches. What does the quantity $85 + x$ represent in the expression? $\newline$ (A)the height of the closet doors and moulding together in inches $\newline$ (B)the perimeter around the outside of the closet doors and moulding in inches $\newline$ (C)the total area of the closet doors and moulding in square inches $\newline$ (D)the area of the moulding in square inches

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Q. Addison, a carpenter, is installing a new set of closet doors with a simple moulding for a client's bedroom. The closet doors are

75

inches wide and

85

inches tall, and the moulding will be an equal width around the sides and top of the doors. The total area of the closet doors and moulding in square inches can be modeled by the expression

(75 + 2x)(85 + x)

, where

x

is the width of the moulding in inches. What does the quantity

85 + x

represent in the expression?

\newline

(A)the height of the closet doors and moulding together in inches

\newline

(B)the perimeter around the outside of the closet doors and moulding in inches

\newline

(C)the total area of the closet doors and moulding in square inches

\newline

(D)the area of the moulding in square inches

Total Area Expression: The expression for the total area is 75 + 2x)(85 + x)\. We know that the first part, \$75 + 2x, represents the total width of the closet doors including the moulding on both sides.
Width and Height Representation: Now, looking at the second part of the expression, $85 + x$ , it must represent the total height of the closet doors including the moulding on the top, since the moulding is of equal width around the sides and top.
Perimeter Calculation: The expression does not represent the perimeter because the perimeter would include the moulding on all four sides and would be calculated differently.
Total Area Calculation: It also does not represent the total area directly, as the total area is the product of the width and height, which is given by the entire expression $(75 + 2x)(85 + x)$ .
Moulding Area Calculation: Lastly, it does not represent the area of the moulding alone because that would require subtracting the area of the doors from the total area.