A wire of length L is cut into two pieces of length X and Y respectively, with Y>X. These pieces are then used to form an upper case "L". If Y/X= (X+Y)/Y, determine the values of X and Y in terms of L.

Answer 1

y/x = (x+y)/y
since x+y=L,
y/x = L/y
Lx = y^2
Lx = (L-x)^2
x^2 - 3Lx + L^2 = 0
now solve as usual for quadratic. I expect you will get only one usable value

Similarly,

Lx = y^2
L(L-y) = y^2
y^2 + Ly - L = 0
now do the same for y.

Make sure you choose positive values such that x+y=L