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.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 2x2+45x+225. What does the quantity 45x+225 represent in the expression?Choices:(A)the area of the museum in square feet(B)the length of the museum and parking lot together in feet(C)the perimeter around the outside of the museum and parking lot in feet(D)the area of the parking lot in square feet
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.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 2x2+45x+225. What does the quantity 45x+225 represent in the expression?Choices:(A)the area of the museum in square feet(B)the length of the museum and parking lot together in feet(C)the perimeter around the outside of the museum and parking lot in feet(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 2x2+45x+225.
Area of Museum: The term 2x2 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 2×15x.
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 15×15.
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.
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