The length of a rectangle is 9 m more than its breadth. If the length is increased by 4 m and the breadth by 3 m, the new area becomes 1190 square metres. What is the original breadth of the rectangle?

\(9\sqrt{15}-8\) m

Let the original breadth be \(x\) m. Then the original length is \(x+9\) m. After the increases, the new length and breadth are \(x+13\) and \(x+3\) m, respectively. Thus, \((x+13)(x+3)=1190\), which gives \(x^2+16x-1151=0\). Using the quadratic formula, \(x=\frac{-16\pm\sqrt{4860}}{2}=-8\pm9\sqrt{15}\). Since a breadth must be positive, the valid value is \(x=-8+9\sqrt{15}\) m; the other root is negative. Exam tip: write the changed dimensions carefully before forming the area equation.

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