A garden is 36 metres long and 24 metres wide. A uniform path runs inside along all four sides. The area of the portion left after making the path is 540 square metres. What is the width of the path?
Answer and explanation
Correct answer: 3 metres
Let the path width be \(x\) metres. The remaining rectangle has length \(36-2x\) and width \(24-2x\). Thus, \((36-2x)(24-2x)=540\), which gives \(x^2-30x+81=0\). Its roots are \(x=3\) and \(x=27\), but the path width must be less than half the garden's breadth, so \(x=27\) is not feasible. Therefore, the correct width is 3 metres. Exam tip: for a path inside all four sides, subtract \(2x\) from each original dimension.
Frequently asked questions
What is the correct answer to this question?
3 metres
Why is this the correct answer?
Let the path width be \(x\) metres. The remaining rectangle has length \(36-2x\) and width \(24-2x\). Thus, \((36-2x)(24-2x)=540\), which gives \(x^2-30x+81=0\). Its roots are \(x=3\) and \(x=27\), but the path width must be less than half the garden's breadth, so \(x=27\) is not feasible. Therefore, the correct width is 3 metres. Exam tip: for a path inside all four sides, subtract \(2x\) from each original 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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