2003 AMC 10A Problem 7

Attempt Problem 7 of the 2003 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

How many non-congruent triangles with perimeter

7

have integer side lengths?

1

2

3

4

5

The three sides are positive integers summing to

7

The longest side must be less than

3.5,

so it is at most

3

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.

Problem 7 in other years