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Equilateral Triangles and Square Root

Source: AMC 12 2008B Problem 24

February 28, 2008
analytic geometryquadraticsAMC

Problem Statement

Let A_0\equal{}(0,0). Distinct points A1,A2,… A_1,A_2,\ldots lie on the x x-axis, and distinct points B1,B2,… B_1,B_2,\ldots lie on the graph of y\equal{}\sqrt{x}. For every positive integer n n, A_{n\minus{}1}B_nA_n is an equilateral triangle. What is the least n n for which the length A0An≥100 A_0A_n\ge100? <spanclass=′latex−bold′>(A)</span> 13<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 17<spanclass=′latex−bold′>(D)</span> 19<spanclass=′latex−bold′>(E)</span> 21 <span class='latex-bold'>(A)</span>\ 13\qquad <span class='latex-bold'>(B)</span>\ 15\qquad <span class='latex-bold'>(C)</span>\ 17\qquad <span class='latex-bold'>(D)</span>\ 19\qquad <span class='latex-bold'>(E)</span>\ 21
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