2008 AMC 10B 第 7 题

Question

一个边长为

10

的等边三角形完全由不重叠的边长为

1

的等边三角形填满。需要多少个小三角形？

An equilateral triangle of side length

10

is completely filled in by non-overlapping equilateral triangles of side length

1.

How many small triangles are required?

10

25

100

250

1000

面积随边长的平方缩放。

Area scales with the square of the side length

大三角形面积是小三角形面积的

10^2

倍。

The big triangle has

10^2

times the area of a small one

大三角形边长是小三角形的

10

倍，所以面积是小三角形的

10^2=100

倍。

因为小三角形无重叠地铺满它，正好需要

100

个。

所以正确答案是 C。

The large triangle has side length

10

times that of a small triangle, so its area is

10^2=100

times as large.

Since the small triangles tile it without overlap, exactly

100

of them are required.

Thus, the correct answer is C.

其他年份的第 7 题