Question

周长为 $7$ 、边长均为整数的互不全等三角形有多少个？

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

$1$

$2$

$3$

$4$

$5$

最长边不能超过 $3$ ，否则另外两边之和不能大于它。

可行的边长只有 $1$ - $3$ - $3$ 和 $2$ - $2$ - $3$ ，因此共有 $2$ 个三角形。

所以正确答案是 B。

The longest side cannot exceed $3,$ since otherwise the other two sides could not reach it.

The only possibilities are side lengths $1$ - $3$ - $3$ and $2$ - $2$ - $3,$ giving $2$ triangles.

Thus, the correct answer is B.