Answer
$3$ feet
Work Step by Step
The area of the rectangular garden and the border is $A_1=(2x+30)(2x+20),$ while the area of the rectangular garden is $A_2=30(20).$ Subtracting the two areas results to the area of the border. Since, the area of the border is given as $336$ square feet, then
\begin{array}{l}\require{cancel}
A=A_1-A_2
\\
336=(2x+30)(2x+20)-30(20)
\\
336=(2x+30)(2x+20)-600
\\
336+600=(2x+30)(2x+20)
\\
936=(2x+30)(2x+20)
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
936=2x(2x)+2x(20)+30(2x)+30(20)
\\
936=4x^2+40x+60x+600
\\
0=4x^2+40x+60x+600-936
\\
4x^2+100x-336=0
\\
\dfrac{4x^2+100x-336}{4}=\dfrac{0}{4}
\\
x^2+25x-84=0
\\
(x+28)(x-3)=0
.\end{array}
Equating each factor to zero (Zero Product Property) then the solutions of the equation above are $
x=\{ -28,3 \}
.$ Since $x$ is a measurement, then only $x=3$ is the acceptable solution. Therefore, the width of the border, $x,$ is $3$ feet.
