2004 · Q84
84. The length of a rectangle is reduced by 20% and breadth is kept constant, and the new figure that is formed is a square.
Consider the following statements :
- 1The area of square is 25% less than the area of rectangle.
- 2The perimeter of square is approximately 11% less than the perimeter of rectangle.
- 3The diagonal of square is approximately 12% less than the diagonal of rectangle.
Which of the statements given above is/are correct?
MathematicsMensuration
- A1 only
- B1 and 2
- C1, 2 and 3
- D2 and 3
Explanation
The new length is 0.8L and the breadth (kept constant) must equal it for a square, so B = 0.8L. Statement 1 is false: the square's area 0.64L² is 20% (not 25%) less than the rectangle's 0.8L². Statement 2 is true: perimeters 3.2L vs 3.6L differ by 11.1% ≈ 11%. Statement 3 is true: diagonals 0.8√2·L ≈ 1.131L vs √1.64·L ≈ 1.281L differ by about 11.7% ≈ 12%. Hence 2 and 3 only.