A uniform path 4 metres wide surrounds a rectangular garden. The garden is 46 metres long and 32 metres wide. What is the area of the entire rectangle, including the path?
Answer and explanation
Correct answer: 2160 square metres
Since the path surrounds the garden on all four sides, add twice its width to each garden dimension: the outer length is \(46+2\times4=54\) m and the outer breadth is \(32+2\times4=40\) m. Therefore, the total area is \(54\times40=2160\) square metres, so option B is correct. Option A results from using incorrect outer dimensions. Exam tip: for a path around all four sides, add \(2\times\) the path width to both dimensions before multiplying.
Frequently asked questions
What is the correct answer to this question?
2160 square metres
Why is this the correct answer?
Since the path surrounds the garden on all four sides, add twice its width to each garden dimension: the outer length is \(46+2\times4=54\) m and the outer breadth is \(32+2\times4=40\) m. Therefore, the total area is \(54\times40=2160\) square metres, so option B is correct. Option A results from using incorrect outer dimensions. Exam tip: for a path around all four sides, add \(2\times\) the path width to both dimensions before multiplying.
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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