Asked by Yin
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.
Answers
Answered by
Steve
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
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
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