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help with geometry

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In the figure, triangles ABC and BCD are equilateral triangles. What is the value of AD / BE when expressed in simplest radical form, where E is the midpoint of BD?

Jan 17, 2021

You might know that 2, 30-60-90 triangles is an equilateral triangle. Now lets name the side of the equilateral triangle $2s$(for simplicity). Now this means the altitude of a single equilateral triangle is $s\sqrt{3}$ that means 2 of these is $2s\sqrt{3}$. This is length AD. Now E is just the midpoint of BD so BE is just $s$. Finally dividing, $\frac{2s\sqrt{3}}{s}=\boxed{2\sqrt{3}}$