A farmer makes a rectangular field with an area of 200 square metres. The length of the field is 5 metres more than its breadth. What is the length of the field?

\(\frac{5(1+\sqrt{33})}{2}\) m

Let the breadth be \(x\) metres. Then the length is \(x+5\) metres, so \(x(x+5)=200\), or \(x^2+5x-200=0\). Using the quadratic formula, \(x=\frac{-5\pm\sqrt{825}}{2}=\frac{5(-1\pm\sqrt{33})}{2}\). Since breadth must be positive, \(x=\frac{5(\sqrt{33}-1)}{2}\) metres. Therefore, the length is \(x+5=\frac{5(1+\sqrt{33})}{2}\) metres, approximately 16.86 metres. The distractor 20 m is incorrect because it would give a breadth of 15 m and an area of 300 square metres. Exam tip: discard the negative root and verify the positive root using the area condition.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.