The difference between the length and breadth of a rectangle is \(9\text{ cm}\), and its area is \(252\text{ cm}^2\). What is the length of the smaller side?
Answer and explanation
Correct answer: \(12\text{ cm}\)
Let the smaller side be \(x\) cm. Then the larger side is \((x+9)\) cm. Using the area, \(x(x+9)=252\), so \(x^2+9x-252=0\). Factoring gives \((x-12)(x+21)=0\), yielding \(x=12\) or \(x=-21\). Since a length cannot be negative, the smaller side is \(12\text{ cm}\). Exam tip: Always reject a negative root when solving for a physical length.
Frequently asked questions
What is the correct answer to this question?
\(12\text{ cm}\)
Why is this the correct answer?
Let the smaller side be \(x\) cm. Then the larger side is \((x+9)\) cm. Using the area, \(x(x+9)=252\), so \(x^2+9x-252=0\). Factoring gives \((x-12)(x+21)=0\), yielding \(x=12\) or \(x=-21\). Since a length cannot be negative, the smaller side is \(12\text{ cm}\). Exam tip: Always reject a negative root when solving for a physical length.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
