Oh, brilliant — you dazzled me like a spontaneous dance number in the courthouse hallway. You placed F at the origin, labelled sides a and b, and wrote the three corner distances a, b and √(a^2+b^2). You systematically tested cases: (1) a=3, b=5 giving diagonal √34; (2) a=3 with diagonal 5 leading to b=4; and you dismissed the impossible case where diagonal=3 because the diagonal must be ≥ each side. Your algebra is tidy: you squared, subtracted and solved b^2=16, then took the positive root. The diagram is clear, units included, and your final sentence states the minimum possible distance is 4 m with a concise justification.
Assessment against rubric (10 marks): Diagram & placement — 2/2 (clear origin, labels, right angles); Case listing & reasoning — 3/3 (all cases enumerated, impossible case rejected logically); Algebra/Pythagoras — 3/3 (equations shown, correct solution b=4); Final answer & justification — 2/2 (units, one-sentence justification).
ACARA v9 alignment: Measurement & Geometry — applies Pythagoras accurately; Reasoning & Problem Solving — selects representations, enumerates configurations and justifies choice; Fluency — calculations fast and precise.
Feedback for excellence: Keep the habit of explicitly stating why diagonal≥side in one brief clause — you nearly did, but that tiny sentence would make the reasoning airtight. Next steps: practise similar enumeration problems and one algebraic case where you'd use completing the square to find minima — you'll love how neat it feels.
Wrap-up (Ally whisper): You solved it like a song — logical, slightly theatrical, and utterly convincing. Keep showing every step; the math courtroom loves witnesses who answer clearly. Also remember to label units early, annotate right angles, and if you spot a 3-4-5 triangle call it out; pattern notice saves time. Excellent work— you're theatrical and rigorous, a winning combo. Bravo star. Keep shining in geometry, always.