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By observation we know:

(Triangle PQR)

(Triangle QRS)

(Triangle BPQ)

We have three equations but 4 unkowns. This is OK since we are not seeking a specific solution but rather a function for L in x [L = f(x)].

Equation [1]

Equation [2]

Equation [3]

The three equations

Solving [1] for y² and [2] for z²

Expanding [3]

Simplifying

Rearranging and squaring both sides

Expanding

Substituting from [1] and [2]

Simplifying

Simplifying

Rearranging

Rearranging

Approved Solution

graphing domain (why?):

Solving the 1st derivative set equal to zero:

(minimizes L and L²)

An investigation shows the maximum and minimum folding options.