Question

Length and breadth of a rectangular sheet of a paper are $20cm$ and $10cm$, respectively. A rectangular piece is cut from the sheet as shown in the given figure. Which of the following statements is correct for the remaining sheet?

(a) Perimeter remains the same but 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 1

Perimeter of rectangular sheet

$=2\times$ (Length + breadth)

$=2\times$(20 + 10)

$=2\times 30$

$=60cm$

$\therefore$ Area $=$ Length$\times$Breadth

$=20\times 10$

$=200c{m}^2$

Now, perimeter of rectangular sheet after cutting the rectangular piece $=$ Sum of all sides

$=20+8+5+2+16+10$

$=60cm$

Area $=$ Area of rectangle $ABFG+$ Area of rectangle $BCDE$

$=$ (Length$\times$Breadth)$+$(Length$\times$Breadth)

$=(15\times 10)+(5\times 8)$

$=150+40$

$=190sqcm$

Hence, perimeter remains the same but area changes after cutting the piece.

Hence, option A is correct.