Question

The length and breadth of the rectangular sheet of paper are 20 cm and 10 cm, respectively as shown in the figure 1.
A rectangular sheet in figure 2 is cut from the corner of the sheet as shown below. Which of the following statements is correct for remaining sheet?

• A. Area remains same but perimeter changes.
• B. Both perimeter and area change.
• C. Both perimeter and area remain same.
• D. Perimeter remains same but area changes.

Answer 1

The correct option is D Perimeter remains same but area changes.

Area and perimeter of figure 1 before figure 2 is cut from it,
Length of the figure = 20 cm
Breadth of the figure = 10 cm
Area of the figure = 20 cm × 10 cm = 200 cm²
Perimeter of the figure = 2(20 cm + 10 cm) = 60 cm

Area and perimeter of figure 1 after figure 2 is cut from it,
Perimeter = 20 cm + 10 cm + 8 cm + 5 cm + 2 cm + 15 cm = 60 cm
Area = Area of figure 1 – Area of figure 2
= 200 cm² – 5 cm × 2 cm = (200 – 10) cm² = 190 cm²

Hence the perimeter of the figure will remain the same but area changes.