The length of a rectangle is 2 metres more than twice its breadth. If its area is \(180\ \text{m}^2\), what is its breadth?
Answer and explanation
Correct answer: \(9\ \text{m}\)
Let the breadth be \(x\) metres. Then the length is \(2x+2\) metres. Using area, \(x(2x+2)=180\), which gives \(x^2+x-90=0\). Factoring, \((x+10)(x-9)=0\), so \(x=9\) or \(x=-10\). Since a length cannot be negative, the breadth is \(9\) metres. Exam tip: In dimension-based problems, reject any negative root as physically meaningless.
Frequently asked questions
What is the correct answer to this question?
\(9\ \text{m}\)
Why is this the correct answer?
Let the breadth be \(x\) metres. Then the length is \(2x+2\) metres. Using area, \(x(2x+2)=180\), which gives \(x^2+x-90=0\). Factoring, \((x+10)(x-9)=0\), so \(x=9\) or \(x=-10\). Since a length cannot be negative, the breadth is \(9\) metres. Exam tip: In dimension-based problems, reject any negative root as physically meaningless.
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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