Measurement applications: design and justify

Task goals

• Given a set of measurement constraints (a range for one dimension, a minimum for another, a target area/volume/cost), invent specific dimensions that satisfy every constraint simultaneously.
• State the chosen dimensions clearly, including a brief justification for why those particular numbers were picked.
• Compute the resulting area, perimeter, volume, or cost from the chosen dimensions -- reusing a technique already learned earlier in the series (rectangle area/perimeter, cuboid volume, Pythagoras' theorem).
• Verify, with an explicit checklist, that every stated constraint is genuinely satisfied by the chosen design.
• Recognise and reason about a genuine trade-off between two or more competing constraints, rather than picking arbitrary compliant numbers.
• Understand that an open-ended design problem has many valid answers, not one single correct answer, and that a response should be marked on its own internal consistency rather than compared against a model answer.
• Compare two different valid designs against an optimisation goal (minimise cost or material, or a stated preference) and justify which is the better choice.
• Communicate a written justification for a design decision that references the actual computed figures, not just intuition.