NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Calculating with rational numbers

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Required skills (click to reveal)

A community garden in Melbourne is divided into rectangular plots. One plot has a length of 13 metres and a width of 26 metres.

A gardener plans to plant vegetables along the perimeter of the plot, leaving a 1-metre-wide path around the inside edge for walking. What is the exact area, in square metres, of the planting region?

Express your answer as a single exact fraction or integer.

Rectangle measurementsLength 13 metres; width 26 metres13 metres26 metres
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Concept illustrations

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Two red counters for every three blue counters. Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.RedRedBlueBlueBlue2 red : 3 blue · 5 counters in all
Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.
Translate a situation into a model. With a fixed charge of $4 and $2 per kilometre, cost C = 4 + 2d. At d = 3 km the cost is $10. Assume this tariff applies for the trip.$4 + $2/kmDefine tariff→C = 4 + 2dBuild rule→d=3 → C=$10Interpret
With a fixed charge of $4 and $2 per kilometre, cost C = 4 + 2d. At d = 3 km the cost is $10. Assume this tariff applies for the trip.

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Formula and explanation (click to reveal)

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The garden plot is rectangular with length 13 m and width 26 m. The planting region is inside the plot, leaving a 1-metre-wide walking path along the inner edge.
  2. The walking path reduces both the length and width of the planting region by 2 metres (1 m on each side).
  3. New length of planting region = 13 m - 2 m = 11 m.
  4. New width of planting region = 26 m - 2 m = 24 m.
  5. Area of a rectangle = length × width. Apply this to the planting region.
  6. Substitute values: area = 11 m × 24 m.
  7. Perform multiplication: 11 × 24 = (10 + 1) × 24 = 10×24 + 1×24 = 240 + 24 = 264.
  8. The area is 264 square metres. This is an integer, so no fraction is needed.
  9. Check: original area = 13 × 26 = 338 m². Path area = 338 - 264 = 74 m². Path is 1 m wide around, so area should be roughly perimeter × 1 m minus corners, but this is not required for the answer.
  10. The planting region has dimensions 11 m by 24 m, so area is 264 m².
  11. Final answer is 264 square metres.
  12. The area of the planting region is exactly 264 square metres.

Reference answer: 264

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