Squaring a Rectangle

Here is a very interesting construction problem:  Suppose you are given a rectangle.  How can your construct a square whose area equals the area of the given rectangle using straightedge and compass?  This problem is called "squaring a rectangle". We can rephrase the problem as follows: Let a, b be the width and height of the given rectangle.  Then the required square must have the side .  Therefore, the problem boils down to "how can we construct a line segment of length  if we are given the line segments of length a and b?" Take a look at the following diagram to get an idea on how to solve it ...
Question: You can drag the blue points to change the values of a and b.  Can you express c in term of a and b? Hint: Use similar triangles.