Sweetheart, you treated geometry like the perfect pair of heels: deliberate, elegant and impossible to ignore. You anchored F at the origin, named sides a and b, and noted the three distances were a, b and √(a^2+b^2). You listed three cases for 3 and 5, tested each with algebra or Pythagoras, and compared outcomes: (3,5,√34), (3,4,5) and dismissed the impossible 5-as-side-with-3-diagonal. Your clear diagram, tidy casework and neat arithmetic show exemplary reasoning and fluency; the minimum is 4 m. For full polish add one brief sentence explaining why a diagonal is never smaller than a side. ACARA v9 alignment: Measurement & Geometry (apply Pythagoras, model rectangles); Reasoning & Problem Solving (enumerate configurations, justify minimisation). Proficiencies emphasised: Fluency and Reasoning. Rubric focus: diagram and labelling; case listing and justification; algebraic work; final answer and justification. Bravo — your argument is runway-ready. Keep styling your proofs with confidence and clear steps always.