2000 AMC 8 Problem 16

Attempt Problem 16 of the 2000 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2000 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

16.

In order for Mateen to walk a kilometer (10001000 meters) in his rectangular backyard, he must walk the length 2525 times or walk its perimeter 1010 times. What is the area of Mateen’s backyard in square meters?
4040
200200
400400
500500
10001000
Answer: C
Concepts:perimeterarea
Small hint:
The length comes from walking it 2525 times
Big hint:
The perimeter comes from walking it 1010 times
Solution:
We can see that the length is 1000÷25=401000 \div 25 = 40 meters, and the perimeter is 1000÷10=1001000 \div 10 = 100 meters.
Note that the perimeter is 22 times the sum of the length and width.
This means that the width is 100÷2−40=10100 \div 2 - 40 = 10 meters, and the area is 40⋅10=40040 \cdot 10 = 400 square meters.
Thus, C is the correct answer.
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