NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Enlargement transformations

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A community garden in Brisbane is planning a new rectangular vegetable plot. The original plot has a length of 97 m and a width of 32 m.

The design is to be enlarged by a scale factor of 3/2 from one of its corners. What is the exact area of the enlarged plot in square metres?

Express your answer as an exact fraction or whole number.

Rectangle measurementsLength 97 m; width 32 m97 m32 m
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Concept illustrations

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Corresponding lengths scale together. The right triangles have side lengths 3,4,5 and 9,12,15. The length scale factor is 3 and the area scale factor is 9. Both use the same drawing scale.34912155×3
The right triangles have side lengths 3,4,5 and 9,12,15. The length scale factor is 3 and the area scale factor is 9. Both use the same drawing scale.
Coordinates on a plane. Illustration: the point (2, 2) lies on y = x. Read x across, then y up.-2-2-1-111223344xy
Illustration: the point (2, 2) lies on y = x. Read x across, then y up.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The original rectangular plot has a length of 97 m and a width of 32 m. The area of a rectangle is given by length × width.
  2. Calculate the original area: 97 m × 32 m = 3104 m².
  3. The plot is enlarged by a scale factor of 3/2. When a shape is enlarged by a scale factor k, the area is multiplied by k².
  4. Compute the square of the scale factor: (3/2)² = 9/4.
  5. Multiply the original area by the area scale factor: 3104 m² × 9/4.
  6. Perform the multiplication: (3104 × 9) / 4.
  7. First compute 3104 × 9: 3104 × 9 = 27936.
  8. Now divide 27936 by 4: 27936 ÷ 4 = 6984.
  9. The area of the enlarged plot is 6984 m².
  10. Verify the calculation: 3104 × 9 = 27936, and 27936 ÷ 4 = 6984. The result is consistent.
  11. The enlargement is applied from one corner, but since it is a uniform scale factor across all dimensions, the area scaling rule still applies exactly.
  12. The exact area of the enlarged plot is 6984 square metres.

Reference answer: 6984 m²

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