Find the largest rhombus that fits in a rectangle?

Question

Given a rectangle with sides of length a and b, where b is the longer side. Let c be the length of the sides of the largest rhombus that fits in the rectangle. Find a formula for c in terms of a and b.

Answer 1

c = (1/2b)(a²+b²), most of the time
Let x = distance from corner to obtuse vertex of the rhombus. Then:
c = b - x
c = √(a² + x²)
That is, we have:
x² = c² - 2cb + b²
x² = c² - a²
Subtract, and solve for c.

Now, I said "most of the time", because I'm not sure it's true for every case. I'll get to you later.

Addendum: It's true.

Answer 2

In a rhombus, all sides are equal whereas in a rectangle, only opposite sides are equal. However, a square is also a rectangle. Thus a rectangle is a rhombus only if its a square. The answer is, therefore, SOMETIMES