The area of the border is equal to
[tex]A=(32+2x)(20+2x)-(32)(20)[/tex]
Expand the equation
[tex]\begin{gathered} A=640+64x+40x+4x^2-640 \\ A=4x^2+104x \end{gathered}[/tex]
Remember that the area of the border is given
A=224 ft2
substitute and solve the quadratic equation
[tex]\begin{gathered} 4x^2+104x=224 \\ 4x^2+104x-224=0 \end{gathered}[/tex]
using the formula
a=4
b=104
c=-224
substitute
[tex]x=\frac{-104\pm\sqrt{104^2-4(4)(-224)}}{2(4)}[/tex][tex]x=\frac{-104\pm120}{8}[/tex]
The values of x are
x=2 ft and x=-28 ft ( is not a solution because is a negative number)
therefore
The answer is 2 ft
