Geometry Practice Test 6

Medians of two equilateral triangles = 3x : 2x
Median = H = $\frac{\sqrt{3}\mathit{a}}{2}$
Median of the bigger equilateral triangle H = $\frac{\sqrt{3}}{2}$ A
Where A is a side
3x = $\frac{\sqrt{3}}{2}\mathit{A}$
A = $\frac{6\mathit{x}}{\sqrt{3}}$
Median of the smaller equilateral triangle = h
= $\frac{\sqrt{3}}{2}\mathit{a}$
2x = $\frac{\sqrt{3}}{2}\mathit{a}$
a = $\frac{4\mathit{x}}{\sqrt{3}}$
Ratio of their sides = A : a
= $\frac{6\mathit{x}}{\sqrt{3}}:\frac{4\mathit{x}}{\sqrt{3}}$
= 6 : 4
= 3 : 2