NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Exploring formulas

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A craft designer is creating a series of rectangular wooden frames for wall art. The formula for the perimeter P of a rectangle is P = 2(l + w), where l is the length and w is the width.

The designer uses a fixed width of 90 cm and varies the length. When the length is 97 cm, what is the exact perimeter of the frame in centimetres?

Express your answer as a whole number or a simplified fraction.

Rectangle measurementsLength 97 cm; width 90 cm97 cm90 cm
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Replace x with its given value. For x = 4, the expression 2x + 3 becomes 2 × 4 + 3 = 11.2x + 3x = 4→2 × 4 + 3Substitute→11Evaluate
For x = 4, the expression 2x + 3 becomes 2 × 4 + 3 = 11.
Keep both sides balanced. The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.x + 614−6−6x = 8
The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The formula for the perimeter of a rectangle is P = 2(l + w). This formula applies to any rectangle where l is the length and w is the width.
  2. The width w is fixed at 90 cm, and the length l is given as 97 cm. These values are substituted into the formula.
  3. Substitute l = 97 and w = 90 into the formula: P = 2(97 + 90).
  4. Add the values inside the parentheses: 97 + 90 = 187.
  5. Multiply the sum by 2: 2 × 187 = 374.
  6. The perimeter is 374 cm. This is a whole number, so no further simplification is needed.
  7. Check the calculation: 2 × (97 + 90) = 2 × 187 = 374. The arithmetic is correct.
  8. Verify units: length and width are in centimetres, so perimeter is in centimetres.
  9. The question asks for the exact perimeter when length is 97 cm and width is 90 cm.
  10. The result 374 cm matches the requirement: it is a whole number and correctly calculated.
  11. The perimeter of the frame is 374 centimetres.
  12. Final answer confirmed: 374 cm.

Reference answer: 374 cm

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