A uniform path of width x metres is built around a garden that is 64 metres long and 44 metres wide. The total area of the garden together with the path is 3996 square metres. What is the value of x?
Answer and explanation
Correct answer: 5 m
The outer dimensions, including the path, are \(64+2x\) metres and \(44+2x\) metres. Thus, \((64+2x)(44+2x)=3996\). On simplification, \(x^2+54x-295=0\), which factors as \((x-5)(x+59)=0\). The roots are \(5\) and \(-59\), but a width cannot be negative, so \(x=5\) metres. Exam tip: for a uniform path around all four sides, add \(2x\) to each original dimension.
Frequently asked questions
What is the correct answer to this question?
5 m
Why is this the correct answer?
The outer dimensions, including the path, are \(64+2x\) metres and \(44+2x\) metres. Thus, \((64+2x)(44+2x)=3996\). On simplification, \(x^2+54x-295=0\), which factors as \((x-5)(x+59)=0\). The roots are \(5\) and \(-59\), but a width cannot be negative, so \(x=5\) metres. Exam tip: for a uniform path around all four 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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