A rectangular field is 30 metres long and 18 metres wide. A path of uniform width is constructed all around the outside of the field. The total area of the field and the path is 748 square metres. What is the width of the path?
Answer and explanation
Correct answer: 2 metres
Let the width of the path be \(x\) metres. Then the outer rectangle has length \(30+2x\) and width \(18+2x\). Thus, \((30+2x)(18+2x)=748\). On simplifying, \(x^2+24x-52=0\), or \((x-2)(x+26)=0\). Since a width must be positive, \(x=2\) metres is the valid answer; \(x=-26\) is not physically meaningful. Exam tip: because the path is added on both opposite sides, add \(2x\) to each original dimension.
Frequently asked questions
What is the correct answer to this question?
2 metres
Why is this the correct answer?
Let the width of the path be \(x\) metres. Then the outer rectangle has length \(30+2x\) and width \(18+2x\). Thus, \((30+2x)(18+2x)=748\). On simplifying, \(x^2+24x-52=0\), or \((x-2)(x+26)=0\). Since a width must be positive, \(x=2\) metres is the valid answer; \(x=-26\) is not physically meaningful. Exam tip: because the path is added on both opposite sides, add \(2x\) to 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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