McClure Sisters Inc., an architectural firm, is in the early phases of planning the building for the Sports and Leisure Museum. The museum will be twice as long as it is wide to accommodate the exhibit hall for sports and the exhibit hall for leisure. The museum will also have a $15$ -foot-wide parking lot along two sides. $\newline$ The total area of the museum and parking lot together in square feet can be modeled by the expression $(2x + 15)(x + 15)$ , where $x$ is the width of the museum in feet. This expression can also be written in the form $2x^2 + 45x + 225$ . What does the quantity $45x + 225$ represent in the expression? $\newline$ Choices: $\newline$ (A)the area of the museum in square feet $\newline$ (B)the length of the museum and parking lot together in feet $\newline$ (C)the perimeter around the outside of the museum and parking lot in feet $\newline$ (D)the area of the parking lot in square feet

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Interpret parts of quadratic expressions: word problems

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Q. McClure Sisters Inc., an architectural firm, is in the early phases of planning the building for the Sports and Leisure Museum. The museum will be twice as long as it is wide to accommodate the exhibit hall for sports and the exhibit hall for leisure. The museum will also have a

15

-foot-wide parking lot along two sides.

\newline

The total area of the museum and parking lot together in square feet can be modeled by the expression

(2x + 15)(x + 15)

, where

x

is the width of the museum in feet. This expression can also be written in the form

2x^2 + 45x + 225

. What does the quantity

45x + 225

represent in the expression?

\newline

Choices:

\newline

(A)the area of the museum in square feet

\newline

(B)the length of the museum and parking lot together in feet

\newline

(C)the perimeter around the outside of the museum and parking lot in feet

\newline

(D)the area of the parking lot in square feet

Total Area Expression: The expression for the total area is $(2x + 15)(x + 15)$ , which expands to $2x^2 + 45x + 225$ .
Area of Museum: The term $2x^2$ represents the area of the museum since the museum is twice as long as it is wide.
Perimeter of Additional Width: The term $45x$ represents the combined perimeter of the additional width due to the parking lot on two sides, which is $15$ feet each, so $2 \times 15x$ .
Area of Parking Lot: The term $225$ represents the area of the parking lot, which is $15$ feet wide along two sides of the museum, so $15 \times 15$ .
Combined Additional Area: Therefore, $45x + 225$ represents the combined additional area due to the parking lot on two sides of the museum.
Correct Choice: The correct choice that matches this description is $(D)$ the area of the parking lot in square feet.