Question

一个矩形牧场要用一段 $100$ 米石墙作为第四边，只在另外三边围栅栏。栅栏上每隔 $12$ 米立一个柱子，包括栅栏与石墙相接处的两个柱子。围出一个 $36$ 米乘 $60$ 米的区域，最少需要多少根柱子？

A rectangular grazing area is to be fenced off on three sides using part of a $100$ meter rock wall as the fourth side. Fence posts are to be placed every $12$ meters along the fence, including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area $36$ m by $60$ m?

$11$

$12$

$13$

$14$

$16$

答案：B

知识点：周长最优化植树问题

难度评级：1030

解答：

当石墙作为较长的 $60$ 米边时，用的柱子最少；此时栅栏覆盖两条 $36$ 米边和一条 $60$ 米边，总路径长 $36 + 60 + 36 = 132$ 米。

每隔 $12$ 米放一根柱子并包括两端，共用 $\dfrac{132}{12} + 1 = 12$ 根柱子。

所以正确答案是 B。

The fewest posts are used when the wall serves as the longer $60$ meter side, so the fence covers two $36$ meter sides and one $60$ meter side, a path of $36 + 60 + 36 = 132$ meters.

Placing a post every $12$ meters, including both ends, uses $\dfrac{132}{12} + 1 = 12$ posts.

Thus, the correct answer is B .

1986 AMC 8 第 18 题

答案：B

难度评级：1030

解答：

其他年份的第 18 题