AMC 8 2000 Problem 16

AMC8 2000 年第 16 题

面积与周长（综合）★★★☆☆

In order for Mateen to walk a kilometer (1000m) 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?

为了让 Mateen 在他的长方形后院里走 1 公里（1000 米），他必须沿着长方形的长走 25 次，或者沿着它的周长走 10 次．那么 Mateen 后院的面积是多少平方米?

A.40
B.200
C.400
D.500
E.1000

正确答案 · Correct Answer

解析 · Solution

Solution 1

The length

L

of the rectangle is

\displaystyle \frac{1000}{25} = 40

meters. The perimeter

P

\displaystyle \frac{1000}{10} = 100

meters. Since

P_{rect} = 2L + 2W

, we plug values in to get:

100 = 2\cdot 40 + 2W

, 100 = 80 + 2W, 2W = 20, W = 10 meters Since

A_{rect} = LW

, the area is

40\cdot 10=400

square meters or

C

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