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?

विकल्प

• 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.

Answer 1

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.