AMC 8 2011 Problem 2

AMC8 2011 年第 2 题

四边形与多边形★☆☆☆☆

Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Whose garden is larger in area?

Karl 的长方形蔬菜园的尺寸是 20 英尺ｘ45 英尺，Makenna 的菜园是 25 英尺ｘ40 英尺。下面哪句话是对的？

A. $\text{Karl''s garden is larger by 100 square feet.}$ / Karl 的菜园大 100 平方英尺
B. $\text{Karl''s garden is larger by 25 square feet.}$ / Karl 的菜园大 25 平方英尺
C. $\text{The gardens are the same size.}$ / 两个菜园一样大
D. $\text{Makenna''s garden is larger by 25 square feet.}$ / Makenna 的菜园大 25 平方英尺
E. $\text{Makenna''s garden is larger by 100 square feet.}$ / Makenna 的菜园大 100 平方英尺

正确答案 · Correct Answer

解析 · Solution

Solution 1

The area of a rectangle is given by the formula length times width. Karl's garden is 20×45 = 900 square feet and Makenna's garden is 25×40 = 1000 square feet. Since 1000 > 900, Makenna's garden is larger by 1000-900=100 square feet.

\Rightarrow \textbf{(E)\ \text{Makenna's garden is larger by 100 square feet.} }

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