A rectangular garden, 50 m long and 36 m wide, is surrounded by a uniform path of width x m. The area of the entire rectangle, including the path, is 2760 square metres. What is the value of x?
Answer and explanation
Correct answer: 5 m
Since the path surrounds the garden on all four sides, the outer dimensions are (50+2x) m and (36+2x) m. Therefore, (50+2x)(36+2x)=2760. Substituting x=5 gives 60×46=2760, so the width of the path is 5 m. The nearby values x=4 and x=6 give areas of 2552 and 2912 square metres, respectively. Exam tip: for a path of width x 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?
Since the path surrounds the garden on all four sides, the outer dimensions are (50+2x) m and (36+2x) m. Therefore, (50+2x)(36+2x)=2760. Substituting x=5 gives 60×46=2760, so the width of the path is 5 m. The nearby values x=4 and x=6 give areas of 2552 and 2912 square metres, respectively. Exam tip: for a path of width x 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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