2015 AMC 12B Problems/Problem 10

Problem

How many noncongruent integer-sided triangles with positive area and perimeter less than 15 are neither equilateral, isosceles, nor right triangles?

$\textbf{(A)}\; 3 \qquad\textbf{(B)}\; 4 \qquad\textbf{(C)}\; 5 \qquad\textbf{(D)}\; 6 \qquad\textbf{(E)}\; 7$

Listing all possible triangle side lengths satisfying the constraints, we find the following:

$\text{2-3-4}\\ \text{2-4-5}\\ \text{2-5-6}\\ \text{3-4-6}\\ \text{3-5-6}$

Thus the answer is $\fbox{\textbf{(C)}\; 5}$ .

2015 AMC 12B (Problems • Answer Key • Resources)
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