#### Answer

The length of a side of the original square is $10 \: meters$.

#### Work Step by Step

Let $x$ be the length of one side of the flower bed, and $x+4$ be the length of the side of the enlarged flower bed.
Get the area of the enlarged flower bed.
$(x+4)^2 = 196$
$x+4 = \sqrt{196}$
$x+4 = 14$
$x = 10 \: meters$