Problem 16 · 2000 AMC 8
Hard
Geometry & Measurement
perimeterarea
In order for Mateen to walk a kilometer (1000 m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?
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Answer: C — 400 square meters.
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Hint 1 of 2
Each '___ times = 1000 m' is secretly a division: if one length is walked 25 times to reach 1000 m, one length is 1000 ÷ 25. Translate both clues into a single number each.
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Hint 2 of 2
Length and perimeter alone don't give area — you need the width. Back it out of perimeter = 2(length + width).
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Approach: turn each 'walk it N times' clue into one measurement
- Length: walked 25 times to cover 1000 m, so one length = 1000 ÷ 25 = 40 m. Perimeter: walked 10 times for 1000 m, so the perimeter = 1000 ÷ 10 = 100 m.
- Perimeter = 2(length + width): 100 = 2(40 + W), so 40 + W = 50 and W = 10 m.
- Area = length × width = 40 × 10 = 400 m².
- The lesson: 'do X to cover a total' clues are just multiplication facts in disguise — divide the total by the count to recover one piece. Then the area needs both dimensions, so use perimeter to fish out the missing one.
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