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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).

Sagot :

The correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

Given that the length of the  floor,x,is atleast 12 feet.The width of the floor is 4 feet less than the length.There is a right angle of height x-4 and base 8 feet. The rectangle inside has length of 8 feet and width be 4 feet.

We are required to find the painted area of the theater room in square feet.

To find the painted area of the theater the following steps must be followed:

1) Find the area of the theater room.

length =x

Breadth=x-4

Area=x(x-4)

=[tex]x^{2} -4x[/tex]

2) Area of the right triangle.

Height=x-4

Base=8

Area=1/2 *8*(x-4)

=4(x-4)

=4x-16

3) Find the area of the rectangle inside labeled closet.

Length=8

Width=4

Area=8*4

=32

Area=Area of theater room-Area of of right triangle-Area of closet.

=[tex]x^{2} -4x[/tex]-4x+16-32

=[tex]x^{2} -8x-16[/tex]

Hence the correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

Learn more about area at https://brainly.com/question/25965491

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