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CEMC Gauss (Grade 7), 1998

Algebra Difficulty 2.0 Junior Find the answer Canada

On a large piece of paper, Dana creates a "rectangular spiral" by drawing line segments of lengths, in cm, of $1, 1, 2, 2, 3, 3, 4, 4, \ldots$ as shown. Dana's pen runs out of ink after the total of all the lengths he has drawn is 3000 cm. What is the length of the longest line segment that Dana draws?

(A) $38$ (B) $39$ (C) $54$ (D) $55$ (E) $30$

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