+230 The diagonals of a regular hexagon have two possible lengths. What is the ratio of the shorter length to the longer length? Express your answer as a common fraction in simplest radical form.
+1639 The diagonals of a regular hexagon have two possible lengths. What is the ratio of the shorter length to the longer length? Express your answer as a common fraction in the simplest radical form.
The ratio is √3 / 2
+14903 The diagonals of a regular hexagon have two possible lengths. What is the ratio of the shorter length to the longer length? Express your answer as a common fraction in simplest radical form.
Hello Ericthegg!
\(c^2=a^2+b^2-2ab\ cos\ 120^0\\ s^2=2\cdot (\frac{d}{2})^2-2\cdot (\frac{d}{2})^2\cdot (-\frac{1}{2})\\ s^2=2\cdot (\frac{d}{2})^2\cdot(1-(-\frac{1}{2}))\\ s^2=3\cdot (\frac{d}{2})^2\)
\(s=\frac{d}{2}\sqrt{3}\)
The ratio is \(\large \frac{s}{d}=\frac{\sqrt{3}}{2}\)
!
