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Q.

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 figure. Which of the following statements is correct for the remaining sheet?


Question Image

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a

Perimeter remains the same but the area changes.

b

Area remains the same but perimeter changes.

c

Both area and perimeter are changing.

d

Both area and perimeter remain the same. 

answer is A.

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Detailed Solution

Given that length and breadth of a rectangular sheet of paper are 20 cm and 10 cm, respectively.
Question ImageQuestion Image By using the formula,
 Perimeter of a rectangle = 2 × (length + breadth)
 = 2 × (20 +10)
 = 2 × 30
 = 60
∴ Perimeter of the rectangular sheet of paper is 60 cm.
Now, to find the perimeter of the rectangular sheet after cutting the rectangular piece
Perimeter = Sum of all sides
= 20+8+5+2+15+10
= 60
∴ Perimeter of the rectangular sheet after cutting the rectangular piece is 60 cm.
To find the area of the rectangle ABCD we will use the formula,
Area = Area of rectangle ABFG + Area of rectangle BCDE
= (length × breadth) + (length × breadth)
= (15 × 10) + (5 × 8)
= 150 + 40
= 190
∴ The area of the rectangle ABCD is 190 sq.cm.
Hence, the perimeter remains the same but the area changes after cutting the piece.
Therefore, option (1) is correct.
 
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