A local school needs to paint the floor of its theater room, where the length of the floor, x, is at least 12 feet. The width of the floor is 4 feet less than the length. It will have a stage and a closet, and the remaining area of the floor will be painted. The dimensions are shown in the diagram:
rectangle with length of x ft and width of x minus 4 ft, right triangle inside labeled stage with height of x minus 4 ft and base of 8 ft, rectangle inside labeled closet with length of 8 ft and width of 4 ft, the rest of the rectangle is labeled floor
Let A represent the painted area, in square feet, of the floor. Choose the correct equation to solve for area (A).
A = x(x − 4) − 0.5(8)(x − 4) − 4(8)
A = x(x − 4) − (8)(x − 4) − 4(8)
A = x(x − 4) + (8)(x − 4) + 4(8)
A = x(x − 4) + 0.5(8)(x − 4) + 4(8)
A = x(x − 4) − 0.5(8)(x − 4) − 4(8) is the correct equation.
This equation calculates the painted area by finding the total area of the floor (x(x-4)), subtracting the area of the stage (0.5(8)(x-4)), and subtracting the area of the closet (4(8)). The remaining area is the painted area.
The correct equation to solve for the area (A) is:
A = x(x − 4) − (8)(x − 4) − 4(8)