Question: A rectangle has side lengths x (length) and y (width) and its diagonals have length 1. Find y as a function of x and then

A rectangle has side lengths x (length) and y (width) and its diagonals have length 1.

  1. Find y as a function of x and then write z = (2x+2y)^2 kxy as a function of x as well, where k is some constant.
  2. For what values of x 0 is y 0? (Rectangles don't have negative side lengths.)
  3. For each value of k find the value (or values) of x in the range of Part (2) where z is maximized. (Careful: It depends on the value of k.)

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