Difference between revisions of "2015 AMC 12B Problems/Problem 10"

Revision as of 10:15, 4 March 2015

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)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

@@ Line 5: / Line 5: @@
 ==Solution==
+Listing all possible triangle side lengths satisfying the constraints, we find the following:
+<math>\text{2-3-4}\\
+\text{2-4-5}\\
+\text{2-5-6}\\
+\text{3-4-6}\\
+\text{3-5-6}
+</math>
+Thus the answer is <math>\fbox{\textbf{(C)}\; 5}</math>.
 ==See Also==
 {{AMC12 box|year=2015|ab=B|num-a=11|num-b=9}}
 {{MAA Notice}}