AMC 8 2012 Problem 17

AMC8 2012 年第 17 题

四边形与多边形★★★☆☆

A square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?

一个边长为整数的正方形被分割成 10 个小正方形，这些小正方形的边长也都是整数，并且至少有 8 个面积为 1．那么原来大正方形的边长的最小值是多少？

A. $\hspace{.05in}3$
B. $\hspace{.05in}4$
C. $\hspace{.05in}5$
D. $\hspace{.05in}6$
E. $\hspace{.05in}7$

正确答案 · Correct Answer

解析 · Solution

Solution 1

The first answer choice

{\textbf{(A)}3}

, can be eliminated since there must be 10 squares with integer side lengths. We then test the next smallest side length, which is 4. The square with area 16 can be partitioned into 8 squares with area 1 and two squares with area 4, which satisfies all the conditions of the problem. Therefore, the smallest possible value of the length of the side of the original square is 4.

继续练习

免费刷 2012 整卷 →