MathDB
Equilateral Triangle

Source: 2015 10A #17

February 4, 2015
geometryperimeteranalytic geometrygraphing linesslopevectortrigonometry

Problem Statement

A line that passes through the origin intersects both the line x=1x=1 and the line y=1+33xy=1+\frac{\sqrt{3}}{3}x. The three lines create an equilateral triangle. What is the perimeter of the triangle?
<spanclass=latexbold>(A)</span>26<spanclass=latexbold>(B)</span>2+23<spanclass=latexbold>(C)</span>6<spanclass=latexbold>(D)</span>3+23<spanclass=latexbold>(E)</span>6+33 <span class='latex-bold'>(A) </span>2\sqrt{6}\qquad<span class='latex-bold'>(B) </span>2+2\sqrt{3}\qquad<span class='latex-bold'>(C) </span>6\qquad<span class='latex-bold'>(D) </span>3+2\sqrt{3}\qquad<span class='latex-bold'>(E) </span>6+\frac{\sqrt{3}}{3}