2015 AMC 10A Problems/Problem 17
A line that passes through the origin in tersects both the line and the line . The three lines create an equilateral triangle. What is the perimeter of the triangle?
Since the triangle is equilateral and one of the sides is a vertical line, the other two sides will have opposite slopes. The slope of one of the other lines is so the other must be . Since this other line passes through the origin, its equation is simply . To find two vertices of the triangle, plug in to both the other equations.
We now have the coordinates of two vertices. and . Apply the distance formula, .