The length of a rectangle is 5 m more than its breadth. If the length is increased by 3 m and the breadth by 2 m, the new area becomes 462 square metres. What was the original breadth of the rectangle?

\(-5+\sqrt{471}\) m

Let the original breadth be \(x\) m. Then the original length is \(x+5\) m. After the increase, the length becomes \(x+8\) m and the breadth becomes \(x+2\) m. Hence, \((x+8)(x+2)=462\), which gives \(x^2+10x-446=0\). Using the quadratic formula, \(x=-5\pm\sqrt{471}\). Since a breadth must be positive, \(x=-5+\sqrt{471}\approx16.70\) m. The distractor 18 m is incorrect because it would give a new area of \(26\times20=520\) square metres. Exam tip: discard the negative root and verify the remaining root in the original area equation.

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