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?

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Perimeter remains the same but the area changes.

Area remains the same but perimeter changes.

Both area and perimeter are changing.

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 Image

By using the formula,
Perimeter of a rectangle = 2

\times

(length + breadth)
= 2

\times

(20 +10)
= 2

\times

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

\times

breadth) + (length

\times

breadth)
= (15

\times

10) + (5

\times

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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