Reading the question more closely this time..ready to take anothe stab at it;
Look at one of the triangles. Right triangle. Call the hypotenuse L, height H, then the base is (W-L)/2.
Use the pythagorean theorum - the sum of the squares of the legs equals the square of the hypotenuse. A little rearrangement gives you:
3L^2 +2LW - H^2 - W^2 = 0
Hey that's one equation, one unknown (L), should be solveable! And it's almost in the form of the quadratic equation,
ax^2 + bx + c = 0, which has the solution (going by memory here)...
x=[-b +/- sqrt(b^2 - 4ac]/2a
Now who's up to doing the math?