Grade 9 Math (MTH1W) · Geometric and Measurement Relationships

Solve optimization problems requiring maximization or minimization of perimeter, area, surface area, or volume, given various constraints

30 tutor-authored questions for this Ontario curriculum expectation, ordered easiest to hardest, every one with a full worked solution. Work through all 30 with your weekly-lesson access code.

Start the 30 questions Curriculum: MTH1W-E1.6

Sample: the first question, solved

Find the rectangle with the smallest possible perimeter, given an area of 36m² (whole-number sides).

📘 Worked solution
6m×6m (a square) → perimeter=24m.

And one from the hard end

"A company wants a rectangular box with a fixed volume of 500cm³ that minimizes cardboard used, with a square base. Set up the relationship between the dimensions, and explain qualitatively why a cube-like shape tends to minimize surface area for a given volume."

Solution shown after you try it in practice mode.

Work through all 30, easiest to hardest

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