2000 AMC 8 Problem 16

Below is the professionally curated solution for Problem 16 of the 2000 AMC 8, 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.

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Concepts:perimeter area

Difficulty rating: 1350

16.

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?

$40$

$200$

$400$

$500$

$1000$

Solution:

We can see that the length is $1000 \div 25 = 40$ m, and the perimeter is $1000 \div 10 = 100$ m.

Note that the perimeter is $2$ times the sum of the length and width.

This means that the width is $100 \div 2 - 40 = 10 \text{ m},$ and the area is $40 \cdot 10 = 400 \text{ m}^2.$

Thus, C is the correct answer.

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