AMC10 2003 A

AMC10 2003 A · Q7

AMC10 2003 A · Q7. It mainly tests Triangles (properties).

How many non-congruent triangles with perimeter 7 have integer side lengths?

周长为 7 的非全等整数边三角形有多少个？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

The longest side cannot be greater than 3, since otherwise the remaining two sides would not be long enough to form a triangle. The only possible triangles have side lengths 1–3–3 or 2–2–3.

最长边不能大于 3，否则其余两边不足以形成三角形。唯一可能的三角形边长为 1–3–3 或 2–2–3。

Topics

GE.002 Triangles (properties)