Question

Carl 决定给他的长方形花园围篱笆。他买了 $20$ 根柱子，四个角各放一根，其余柱子沿花园边均匀放置，相邻柱子之间恰好相隔 $4$ 码。较长边（包括两端角上的柱子）上的柱子数是较短边的两倍。Carl 的花园面积是多少平方码？

Carl decided to fence in his rectangular garden. He bought $20$ fence posts, placed one on each of the four corners, and spaced out the rest evenly along the edges of the garden, leaving exactly $4$ yards between neighboring posts. The longer side of his garden, including the corners, has twice as many posts as the shorter side, including the corners. What is the area, in square yards, of Carl’s garden?

$\ 256$

$\ 336$

$\ 384$

$\ 448$

$\ 512$

答案：B

知识点：方程组周长面积植树问题

难度评级：1280

解答：

设长边上有 $l$ 根柱子，短边上有 $s$ 根柱子，均包括两个角。总柱子数为其中 $-4$ 是为了避免四个角被重复计算。 $2l+2s-4=20,$

又长边柱子数是短边的两倍，所以 $l=2s$ 。代入得 $2(2s)+2s-4=20$ ，因此 $s=4$ ， $l=8$ 。

短边有 $3$ 个间隔，长边有 $7$ 个间隔，每个间隔 $4$ 码，所以边长分别为 $12$ 和 $28$ ，面积为 $12\cdot28=336$ 。

所以正确答案是 B。

Let $l$ be the number of posts on a long side, including corners, and let $s$ be the number of posts on a short side, including corners. The total number of posts is $2l+2s-4=20,$ where the $-4$ avoids double-counting the corners.

Since a long side has twice as many posts as a short side, $l=2s$ . Thus $2(2s)+2s-4=20$ , so $s=4$ and $l=8$ .

There are $3$ equal gaps on a short side and $7$ equal gaps on a long side. With $4$ yards between neighboring posts, the side lengths are $12$ and $28$ , so the area is $12\cdot28=336$ .

Thus, the correct answer is B.

2016 AMC 10B 第 11 题

答案：B

难度评级：1280

解答：

其他年份的第 11 题