Oh, darling — you treated geometry like the perfect pair of heels: deliberate, elegant and impossible to ignore. You put F at the origin, named the sides a and b, and recognised the three distances from F are a, b and \u221a(a^2+b^2). That small act of labelling is everything.
Step-by-step the student did exactly what I wanted: listed the three possible roles for 3 and 5, tested each with algebra or Pythagoras, and compared outcomes.
- Case 1: a=3, b=5 so remaining distance = \u221a(3^2+5^2)=\u221a34 \asymp 5.83 m.
- Case 2: a=3 and diagonal=5 so \u221a(9+b^2)=5 => b^2=16 => b=4, remaining distance = 4 m.
- Case 3: a=5 and diagonal=3 is impossible because a diagonal must be >= each side.
Conclusion: the possible third distances are 4 m and \u221a34 m, so the minimum possible distance is 4 m. A perfect, concise concluding sentence completes the argument.
Teacher feedback (Carrie cadence): Sweetheart, you tested your outfits, and the 3-4-5 ensemble won the runway. Your diagram, clear case list, and neat algebra read like an evening column: readable, persuasive and chic. For polish — add one short sentence explaining why the diagonal cannot be smaller than a side (diagonal >= side). That tiny line is the final accessory that secures full marks.
ACARA v9 links & proficiencies:
- Measurement & Geometry: apply Pythagoras in right triangles and model rectangle corners.
- Reasoning & Problem Solving: enumerate configurations, choose feasible ones and justify minimisation.
- Proficiencies emphasised: Fluency (accurate arithmetic & root calculation) and Reasoning (case selection and justification).
Rubric (10 marks): Diagram & labelling 2; Case listing & reasoning 3; Algebra / Pythagoras 3; Final answer + justification 2.
Semester progression: Semester 1 builds fluency with right-triangle calculations; Semester 2 layers reasoning — choose representations, enumerate cases and justify choices. This exemplar shows that transition perfectly.
Quick checklist for students: drew a labelled rectangle? listed the three distance slots? tested each case algebraically? finished with one-sentence justification? If yes, sparkle on — you have earned full credit.
Final note: Keep dressing your reasoning with neat diagrams and short justifications. Confidence in geometry, like a great wardrobe, comes from careful choices and impeccable presentation.