Answer:
The room is 9 feet long.
Step-by-step explanation:
Lets take the width of the room as [tex]x[/tex] feet.
Then, the length of the room will be [tex]x+3[/tex] feet.
Are of a rectangle = Length * Width
⇒[tex]54=x*(x+3)[/tex]
⇒[tex]54=x^{2} +3x[/tex]
⇒[tex]0=x^{2} +3x-54[/tex]
⇒[tex]x^{2} +3x-54=0[/tex]
⇒[tex]x^{2} +9x-6x-54=0[/tex]
⇒[tex]x(x+9)-6(x+9)=0[/tex]
⇒[tex](x+9)(x-6)=0[/tex]
Thefore either,
[tex]x+9=0[/tex] or [tex]x-6=0[/tex]
[tex]x=-9[/tex] or [tex]x=6[/tex]
[tex]x[/tex] is the width of the room, so a width cannot have a negative value. So we take the positive value.
Therefore,
[tex]x=6[/tex] ⇒ Width of the room is 6 feet.
Length of the room = [tex]x+3[/tex] = [tex]6+3[/tex]=9 feet.
Therefore the room is 9 feet long.
