01 Minimum length of cables linking to one point

$L = L_1 + L_2 + L_3$

$L = \sqrt{2^2 + y^2} + \sqrt{3^2 + y^2} + (5 - y)$

$L = \sqrt{4 + y^2} + \sqrt{9 + y^2} + 5 - y$
 

 

$\dfrac{dL}{dy} = \dfrac{2y}{2\sqrt{4+y^2}} + \dfrac{2y}{2\sqrt{9+y^2}} - 1 = 0$

$y = 1.407 ~ \text{m}$
 

$L_3 = 5 - y$

$L_3 = 5 - 1.407$

$L_3 = 3.593 ~ \text{m}$           answer