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Question
Length and breadth of a rectangular sheet of paper are 20 cm and 10 cm, respectively. A rectangular piece is cut from the sheet as shown in the following figure. Which of the following statements is correct for the remaining sheet?
Options
Perimeter remains same but area changes.
Area remains the same but perimeter changes.
Both area and perimeter are changing.
Both area and perimeter remain the same.
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Solution
Perimeter remains same but area changes
Explanation:
Perimeter of rectangular sheet = 2 × (Length + Breadth)
= 2 × (20 + 10)
= 2 × 30
= 60 cm
∴ A × Breadth = 200 cm2 
Now, perimeter of rectangular sheet after cutting the rectangular piece
= Sum of all sides
= 20 + 8 + 5 + 2 + 15 + 10
= 60 cm
Area = Area of rectangle ABFG + Area of rectangle BCDE
= (Length × Breadth) + (Length × Breadth)
= (15 × 10) + (5 × 8)
= 150 + 40
= 190 sq cm
Hence, perimeter remains the same but area changes after cutting the piece.
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