We assume the triangle is a right triangle. In a 30°-60°-90° triangle, the longest side is twice the length of the shortest.
... 4x = 2(√(x/2))
... 2x = √(x/2) . . . . . . divide by 2
... 4x² = x/2 . . . . . . . . square both sides
... 8x² - x = 0 . . . . . . . multiply by 2, subtract x
... x(8x -1) = 0 . . . . . . . factor
... x = 0 . . . or . . . x = 1/8 . . . . . . values of x that make the factors zero
The first case (x=0) is a "degenerate" case and is not useful. The entire triangle is a single point in that case.
The value of x is ...
... x = 1/8
