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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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