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

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A rectangular training mat in Adelaide has a length of 24 m and a width of 87 m. It is enlarged by a scale factor of 3/2 from one of its corners.

What is the exact area of the enlarged mat in square metres? Express your answer as an exact fraction or whole number.

Rectangle measurementsLength 24 m; width 87 m24 m87 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

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Worked solution

  1. The original rectangular training mat has a length of 24 m and a width of 87 m. The area of a rectangle is calculated as length × width.
  2. Calculate the original area: 24 m × 87 m = 2088 m².
  3. The mat is enlarged by a scale factor of 3/2. When a shape is enlarged by a scale factor, the area scales by the square of the scale factor.
  4. The area scaling factor is (3/2)² = 9/4.
  5. Multiply the original area by the area scaling factor: 2088 m² × 9/4.
  6. First, divide 2088 by 4: 2088 ÷ 4 = 522.
  7. Then, multiply 522 by 9: 522 × 9 = 4698.
  8. The area of the enlarged mat is 4698 m².
  9. Verify by calculating the new dimensions: new length = 24 × 3/2 = 36 m, new width = 87 × 3/2 = 130.5 m.
  10. Calculate the new area: 36 m × 130.5 m = 4698 m².
  11. The result matches, confirming the area is exactly 4698 square metres.
  12. The exact area of the enlarged mat is 4698 m².

Reference answer: 4698 m²

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