Question

A rectangular paper of \( 20 \, \text{cm} \times 8 \, \text{cm} \) is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is:

• A. \( 18 \)
• B. \( 24 \)
• C. \( 20 \)
• D. \( 21 \)

Hint:

When solving folding problems, carefully track the dimensions after each fold and ensure you apply the perimeter formula correctly based on the final dimensions.

Answer 1

The Correct Option is A

Step 1: Determine the dimensions of the paper after folding.
The original dimensions of the rectangular paper are \( 20 \, \text{cm} \times 8 \, \text{cm} \). Fold 1: Folding along the line of symmetry perpendicular to the longer edge reduces the length by half: \[ \text{New dimensions: } 10 \, \text{cm} \times 8 \, \text{cm}. \] Fold 2: Folding again perpendicular to the longer edge reduces the new length by half: \[ \text{New dimensions: } 5 \, \text{cm} \times 8 \, \text{cm}. \] Fold 3: Folding a third time perpendicular to the longer edge reduces the new length by half: \[ \text{New dimensions: } 2.5 \, \text{cm} \times 8 \, \text{cm}. \] Step 2: Calculate the perimeter of the final folded sheet.
The perimeter of a rectangle is given by: \[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}). \] Substituting the dimensions \( 2.5 \, \text{cm} \) and \( 8 \, \text{cm} \): \[ \text{Perimeter} = 2 \times (2.5 + 6) = 2 \times 9 = 18 \, \text{cm}. \] Conclusion: The perimeter of the final folded sheet is \( 18 \, \text{cm} \).