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:

For folding problems, halve the relevant dimension at each fold, then compute the perimeter of the final folded rectangle.

Answer 1

The Correct Option is B

Step 1: Initial dimensions.
The rectangle is \(20 \, \text{cm}\) (length) and \(8 \, \text{cm}\) (width). Folding is always perpendicular to the long edge, so each fold halves the length.
Step 2: Successive folds.
- After 1st fold: length \(20/2 = 10\) cm, width \(8\) cm.
- After 2nd fold: length \(10/2 = 5\) cm, width \(8\) cm.
- After 3rd fold: length \(5/2 = 2.5\) cm, width \(8\) cm.
Final folded dimensions: \(2.5 \, \text{cm} \times 8 \, \text{cm}\).
Step 3: Perimeter.
Perimeter \(= 2 \times (2.5 + 8) = 2 \times 10.5 = 21\) cm. But wait—perimeter after folding means the folded sheet is layered, so only the outside boundary matters. The outside is still a rectangle \(2.5 \times 8\).
\(\Rightarrow\) Perimeter \(= 21\) cm. Correction: Careful re-check shows option (D) 21 is correct. \[\boxed{21}\]