The area of the rectangular field is \(60x80 = 4800\). \(\)

After the farmer plowed the borders, the unplowed dimension would be: width = \(60-2x\) and length = \(80-2x\), where \(x\) is the width of the boder

Thus, \(4800 = 2(60-2x)(80-2x)\)

\(4800 = 2(4800 - 280x + 4x^2)\)

\(0 = 4800 -560x + 8x^2\)

\(x_1 = \frac{560 + \sqrt{560^2 -4(8)(4800)}}{16}\)

\(x_1 = 60\)

\(x_2 = \frac{560 - \sqrt{560^2 -4(8)(4800)}}{16}\)

\(x_2 = 10\)

By checking the values of \(x's\) the width of the border is \(10\) rods.