Consider percent increases in increments of ten: 10%, 20%, 30%, etc. Suppose both sides of a rectangle are increased by the same percent. What is the first "multiple of ten" percent increase that would double the area?
The multipliers for these percent increases would be: 1.1, 1.2, 1.3, etc. Since each side, L and W, will be multiplied by this, the area will be multiplied by this factor squared.
(1.1)2=1.21, a 21% increase in area
(1.2)2=1.44, a 44% increase in area
(1.3)2=1.69, a 69% increase in area
(1.4)2=1.96, a 96% increase in area
(1.5)2=2.25, a 125% increase in area
This last one, a 50% increase, is the first that more than doubles the area.