A composite figure is formed by removing a 3 cm × 4 cm rectangle from the corner of a 10 cm × 8 cm rectangle. What is the perimeter of the resulting composite figure?
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Worked Solution
Step 1: Original perimeter = 2 × (10 + 8) = 36 cm.
Step 2: When the 3 × 4 corner notch is removed, trace the new boundary:
- Top: 10 cm
- Right (reduced): 8 − 4 = 4 cm
- Notch horizontal step: 3 cm (inward)
- Notch vertical step: 4 cm (downward)
- Bottom (reduced): 10 − 3 = 7 cm
- Left: 8 cm
Total = 10 + 4 + 3 + 4 + 7 + 8 = 36 cm.
Step 3: The two removed outer corner edges (3 cm and 4 cm) are exactly replaced by the two new inner notch edges (3 cm and 4 cm). Net change = 0.
Perimeter of composite figure = 36 cm.
Correct answer: 36 cm
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