Answer
$3\ ft$
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ is the width of the strip. We assume that all the $168$ plants will be used, which gives a total strip area of $168\ ft^2$
Step 2. The dimensions of the larger rectangle are $10+2x$ by $12+2x$, and the area of the strip is given by the difference between the larger and smaller rectangles; we have $(10+2x)(12+2x)-10\times12=168$
Step 3. Simplify the above equation to get $(10+2x)(12+2x)=288$, $(5+x)(6+x)=72$, $x^2+11x+30=72$ and finally $x^2+11x-42=0$
Step 4. Solve the above equation by factoring to get $(x-3)(x+14)=0$. Discard the negative solution to get $x=3\ ft$.
