A path around a lawn
One border width, applied twice per dimension, carried through to a count of bags.
Scenario
A rectangular lawn measures 24 m by 15 m.
A gravel path of uniform width 2 m is laid all the way around the outside of the lawn, so that the lawn sits centred inside the paved rectangle.
Answers in order, explanations withheld, and a report on where the chain broke.
- 15.1AreaFoundation
What is the area of the lawn?
- A360 square metres
- B78 square metres
- C39 square metres
- D720 square metres
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360 square metres
Area is length times width: 24 x 15 = 360 square metres. The choice 78 is the perimeter and 39 is the sum of the two sides, neither of which measures a surface.
- 15.2AreaStandard
What are the dimensions of the outer rectangle formed by the lawn and the path together?
- A28 m by 19 m
- B26 m by 17 m
- C48 m by 30 m
- D26 m by 19 m
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28 m by 19 m
The path runs along both ends of each dimension, so each gains 2 m twice: 24 + 4 = 28 and 15 + 4 = 19. Adding the width once gives 26 by 17, which is the single error this whole set is built to expose.
- 15.3AreaChallenge
Builds on: Questions 1 and 2, and it is the first point at which the error in question 2 becomes visible — as a difference of two areas rather than as an odd-looking length.
What is the area of the path alone?
- A172 square metres
- B82 square metres
- C532 square metres
- D156 square metres
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172 square metres
The path is what is left when the lawn is removed from the outer rectangle: 28 x 19 = 532, and 532 - 360 = 172 square metres. Note where the wrong dimensions land you: 26 x 17 = 442, and 442 - 360 = 82, a number that looks perfectly reasonable on its own.
- 15.4RatesChallenge
Builds on: The 172 square metres from question 3. Carrying the 82 forward instead gives 33 bags — an answer that is wrong by half and gives no sign of it.
Gravel is sold in bags that cover 2.5 square metres, and bags cannot be split. How many bags are needed?
- A69
- B68
- C70
- D68.8
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69
172 / 2.5 = 68.8, and since a bag cannot be split the count rounds up to 69. Sixty-eight bags cover 170 square metres, leaving 2 square metres bare, which is why rounding down is not an option here.