# Analyzing an uncertain triangle

Geometry Level 4

Given that $$\Delta ABC$$ with perimeter of 1 has side lengths which are in a nonzero arithmetic progression.

Which of the following statements is/are true?

• A. The length of the second side is $$\frac{1}{3}$$.
• B. The common difference between consecutive sides is greater than the length of the smallest side.
• C. The common difference cannot be equal the length of the smallest side
• D. The length of the longest side takes at least half of the perimeter.
• E. The lengths of the sides and the common difference need not be rational.
• F. No triangle as described above can exist.
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