Why the statement is false
- Let the side be (a).
Original area = side × side = (a imes a).
So, original area = (a^2).
- Now double the side.
New side = (2a).
- Find the new area.
New area = new side × new side = ((2a) imes (2a)).
= (2 imes 2 imes a imes a).
= (4 imes a^2).
So, new area = (4a^2).
- Compare the areas.
Original area = (a^2).
New area = (4a^2).
Therefore, new area = (4 imes) the original area (four times), not double.
Quick number check:
If (a = 5) cm, original area = (5 imes 5 = 25 ext{cm}^2).
New side = (10) cm, new area = (10 imes 10 = 100 ext{cm}^2).
(100 = 4 imes 25), so the area becomes four times.