Answer
$3\ ft$
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ is the width of the border.
Step 2. The dimensions of the larger rectangle are $20+2x$ by $30+2x$, and the area of the border is given by the difference between the larger and smaller rectangles; we have $(20+2x)(30+2x)-20\times30=336$
Step 3. Simplify the above equation to get $(20+2x)(30+2x)=936$, $(10+x)(15+x)=234$, $x^2+25x+150=234$ and finally $x^2+25x-84=0$
Step 4. Solve the above equation by factoring to get $(x-3)(x+28)=0$. Discard the negative solution to get $x=3\ m$.
