Answer:
Length is 24 feet and width is 9 feet.
Step-by-step explanation:
It is given that length of a rectangular wall is 6 feet longer than twice its width.
Let x feet be the width of wall.
Length = 2x+6 feet
Area of rectangle is
[tex]A=length \times width[/tex]
[tex]A=(2x+6)\times x[/tex]
[tex]A=2x^2+6x[/tex]
It is given that area of a rectangular wall of a barn is 216 square feet.
[tex]2x^2+6x=216[/tex]
[tex]x^2+3x=108[/tex]
[tex]x^2+3x-108=0[/tex]
Splitting the middle term, we get
[tex]x^2+12x-9x-108=0[/tex]
[tex]x(x+12)-9(x+12)=0[/tex]
[tex](x+12)(x-9)[/tex]
[tex]x=-12,9[/tex]
Width can not be negative. So width is 9 feet.
Length [tex]=2(9)+6=18+6=24\text{ feet}[/tex]
Therefore, length is 24 feet and width is 9 feet.
