A 6-foot-wide hallway is painted as shown, using equal amounts of white and black paint.a. How long is the hallway?b. Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint? Explain.

we know thatThe hallway is painted using equal amounts of white and black paintsoTo know the amount of white paint------> calculate the area of white paint[tex]A=5x*6=30x\ ft^{2}[/tex]To know the amount of black paint------> calculate the area of black paint[tex]A=(x+1)*4*6=(24+24x)\ ft^{2}[/tex]equate the areas[tex]30x=(24+24x)\\30x-24x=24\\6x=24\\x=4\ ft[/tex]Find the length of the hallway[tex]5x+(4x+4)=9x+4=9*4+4=40\ ft[/tex]thereforethe answer part a) isThe hallway is [tex]40\ ft[/tex] longPart b) Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint?we know thatthe amount of white paint is [tex]30x\ ft^{2}[/tex]if the black paint is twice that the white paintthenamount of black paint is [tex]2*30x=60x\ ft^{2}[/tex]amount of black paint with the same pattern is [tex](24+24x)\ ft^{2}[/tex]equate (24+24x)\ ft^{2}=(60x)\ ft^{2}solve for the new value of x[tex]24x+24=60x\\ 60x-24x=24\\ x=24/36\\x= 2/3\ ft[/tex]Find the new length of the hallway[tex]5x+(4x+4)=9x+4=9*(2/3)+4=10\ ft[/tex]thereforethe answer isYes, the same hallway can be painted with the same pattern, using twice as much black paint as white paint, but the hallway decreases in length