1956 AHSME Problems/Problem 43

Problem 43

The number of scalene triangles having all sides of integral lengths, and perimeter less than $13$ is:

$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 18$

Solution

We can write all possible triangles adding up to 12 or less \[(2, 4, 5)=11\] \[(3, 4, 5)=12\] \[(2, 3, 4)=9\]

This leaves $\boxed{\textbf{(C)} \quad 3}$ scalene triangles.

-coolmath34

-rubslul

(If you see any cases I missed out, edit them in.)

See Also

1956 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 42
Followed by
Problem 44
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