A rectangular field is 16 m …

Let the width of the path be x meters,
We know that, if length of rectangle = l, width of rectangle =b & width of path around it x then,
Area of path = {tex}lb\;-(l-2x)(b-2x){/tex}
{tex}\Rightarrow{/tex}16 {tex}\times{/tex} 10 - (16 - 2x)(10 - 2x) = 120
{tex}\Rightarrow{/tex} 16 {tex}\times{/tex} 10 - {160 - 32x - 20x + 4x²} = 120
{tex}\Rightarrow{/tex} 160 - 160 + 32x + 20x - 4x² = 120
{tex}\Rightarrow{/tex} -4x² + 52x - 120 = 0
{tex}\Rightarrow{/tex} 2x² - 26x + 60 = 0 
{tex}\Rightarrow{/tex} x² - 13x + 30 = 0
{tex}\Rightarrow{/tex} x² - 10x - 3x + 30 = 0 {tex}\Rightarrow{/tex} x(x - 10) - 3(x - 10) = 0
{tex}\Rightarrow{/tex} (x - 10) (x - 3) = 0
{tex}\Rightarrow{/tex} x - 10 = 0 or x - 3 = 0
But x ≠10 ,as width of path can't be greater than width of rectangle. So, x = 3m
Hence, the width of the path = 3 m