FORMULABANK

Hypothesis:

When you double both sides of a rectangle, the area will always be four times larger.

We start with a rectangle where the sides are 4 and 3.

Area: $4\cdot 3=12$

Doubling the sides: $8\cdot 6=48$, and $48/12=4$

Here, it works, but I can't be sure it's true for all cases.

Using algebra:

$a\cdot b\cdot 4=2\cdot a\cdot 2\cdot b$

Reducing:

$a\cdot b\cdot 4=a\cdot b\cdot 4$

There is a match, and thus it is proven.