A uniform path is constructed all around inside a rectangular grassy plot that is 30 m long and 20 m wide. The area of the remaining grassy portion is 416 m². What is the width of the path?

Correct answer: 2 m

Let the width of the path be \(x\) m. The dimensions of the remaining grassy rectangle are \((30-2x)\) m and \((20-2x)\) m. Thus, \((30-2x)(20-2x)=416\), which gives \(x^2-25x+46=0\), or \((x-2)(x-23)=0\). The root \(x=23\) m is not possible because the path width must be less than half the breadth, so the valid value is \(x=2\) m. Exam tip: for a path inside all four sides, subtract \(2x\) from both original dimensions.