The area of a rectangular room is 432 square units, and its length is 6 units more than its breadth. What is the breadth of the room?
Answer and explanation
Correct answer: 18
Let the breadth be \(x\) units. Then the length is \(x+6\) units, so the area gives \(x(x+6)=432\), or \(x^2+6x-432=0\). Factoring, \((x+24)(x-18)=0\), so \(x=18\) or \(x=-24\). Since a length cannot be negative, the breadth is 18 units. Exam tip: Reject any negative root when solving for a physical dimension.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Let the breadth be \(x\) units. Then the length is \(x+6\) units, so the area gives \(x(x+6)=432\), or \(x^2+6x-432=0\). Factoring, \((x+24)(x-18)=0\), so \(x=18\) or \(x=-24\). Since a length cannot be negative, the breadth is 18 units. Exam tip: Reject any negative root when solving for a physical dimension.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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