Using Pythagoras' theorem the diagonal brace needs to be 15 feet

If, by sturdy, you mean rigid, the answer is no. Without a diagonal brace, a square can easily be distorted into a rhombus.

A diamond is not a rigid shape unless it has a brace. A brace is a diagonal line you put inside shapes to make them rigid. Triangles are rigid so if you put a brace in a square to make two triangles the square is now rigid.

What is the answer to brace your self 1-6 chapter1