If you double the length of all 4 sides, the area is increased 4 times...
Let's try to prove it via some examples:
1. Let sides of a ractangle be 2 and 3 mt.
So, the area (length x breadth) = 6 mt.
2. Let sides of a ractangle be 4 and 6 mt. (2x2 and 3x2)
So, the area (length x breadth) = 24 mt.
3. Let sides of a ractangle be 8 and 12 mt. (4x2 and 6x2)
So, the area (length x breadth) = 96 mt.
From example 1 and 2, we get
24/6 = 4
And, example 2 and 3, we get
96/24 = 4
Hence proved