Answer
The length of a side of the original square is $7 \: meters$.
Work Step by Step
Let $x$ be the length of one side of the square flower bed, and $x+8$ be the length of the side of the enlarged flower bed.
Get the area of the enlarged flower bed.
$(x+8)^2 = 225$
$x+8 = \sqrt{225}$
$x+8 = 15$
$x = 7 \: meters$
