Question

Length and breadth of a rectangular sheet of paper are $\text{20cm, and 10 cm}$ respectively. A square piece is cut from the sheet as shown in the figure below. Which of the following statement is correct for the remaining sheet.

• A. Area remains the same but perimeter changes.
• B. Perimeter remains the same but area changes
• C. Both perimeter and area are changing
• D. Both perimeter and area remains same.

Answer 1

The correct option is B

Perimeter remains the same but area changes

Step 1: Calculating Area and Perimeter of rectangular sheet-

The length of the rectangular sheet = $\text{20 cm}$

The breadth of the rectangular sheet = $\text{10 cm}$

Area of the rectangular sheet = ${\text{length ×breadth = 20×10 = 200 cm}}^2$

The perimeter of the rectangular sheet = $\text{2×(length+breadth) = 2×(20+10) = 2×30 = 60 cm}$

Step 2: Calculating Area and Perimeter of new shape -

After removing the square sheet of side length $\text{5 cm}$, new shape looks like -

Area of new shape = Original area of the rectangular sheet - Area of square sheet

= ${\text{200 - (5×5) = 200-25 = 175 cm}}^2$

The perimeter of the new shape = Sum of all the sides

= $\text{20+5+5+5+15+10 = 60 cm}$

Hence, we can clearly see that the area of the shape changes but perimeter remains same.