Question

一个三角形的三边长度（单位为英寸）是三个连续整数。最短边长度是周长的 $30\%$ 。最长边长度是多少？

The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is $30\%$ of the perimeter. What is the length of the longest side?

$\ 7$

$\ 8$

$\ 9$

$\ 10$

$\ 11$

答案：E

知识点：周长一次方程百分数

难度评级：1060

解答：

设最短边长为 $s$ 。三边长度为 $s,s+1,s+2$ ，周长为 $3s+3$ 。因为 $s = 0.3(3s+3)$ ，所以 $s = 0.9s + 0.9$ 。因此 $0.1s = 0.9$ ，得到 $s = 9$ ，最长边为 $s + 2 = 11$ 。

所以正确答案是 E。

Let $s$ be the smallest length. Then, all the side lengths are $s,s+1,s+2.$ This would make the perimeter equal to $3s+3.$ Since $s = 0.3(3s+3),$ then $s = 0.9s + 0.9 .$ This makes $0.1s = 0.9,$ so $s = 9$ which makes the longest side length $s + 2 = 11.$

Thus, the answer is E .

2010 AMC 8 第 13 题

答案：E

难度评级：1060

解答：

其他年份的第 13 题