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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.)A = x(x − 4) − 0.5(8)(x − 4) − 4(8)
B.)A = x(x − 4) − (8)(x − 4) − 4(8)
C.)A = x(x − 4) + (8)(x − 4) + 4(8)
D.)A = x(x − 4) + 0.5(8)(x − 4) + 4(8)

Respuesta :

Answer: The correct equation is the option A.)A = x(x − 4) − 0.5(8)(x − 4) − 4(8)

Step-by-step explanation:

To find the painted area of the theater room in square feet, the following steps must be followed:

1. Determine the area of the theater room

Length: x

Width: x-4

A (theater room) = x (x-4)

2. Determine the area of the right triangle

Height: x-4

Base: 8

A (right triangle) = 0.5 (8) (x-4)

3. Determine the area of the rectangle inside labeled closet

Length: 8

Width: 4

A (closet) = 8 (4)

4. The area to be painted will be the substraction between the total area of the theater room, less the area of the right triangle and less the area of the rectangle of the closet like this:

A= A(theater room) - A(right triangle) - A (closet)

A = x (x-4) -0.5 (8) (x - 4) - 4 (8)

Therefore, the correct equation to solve by area is option A

qwerty1128

Answer: A

Step-by-step explanation: I took le test

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