A farmer uses 120 metres of fencing to enclose a rectangular field on all four sides. If the area of the field is 875 square metres, what are its length and breadth?

Correct answer: 25 m and 35 m

The perimeter of the rectangle is 120 m, so \(2(l+b)=120\), giving \(l+b=60\). Its area gives \(lb=875\). If one dimension is \(x\), the other is \(60-x\), so \(x(60-x)=875\). Thus \(x^2-60x+875=0\), whose roots are 25 and 35. Therefore, the dimensions are 25 m and 35 m. Option A gives an area of 800 square metres, while option C gives 900 square metres. Exam tip: In fencing problems, form the perimeter equation first and the area equation second.