Question 14701
You are doing fine so far.

{{{2x^2 + 6x + 9 = 225}}} Subtract 225 from both sides.
{{{2x^2 + 6x - 216 = 0}}} Factor a 2 just to make process a little easier.
{{{2(x^2 + 3x - 108) = 0}}} Factor the parentheses.
{{{2(x - 9)(x + 12) = 0}}} Apply the zero products principle.
{{{(x - 9) = 0}}} or {{{x + 12 = 0}}}
If x - 9 = 0, then x = 9
If x + 12 = 0, then x = -12 Discard this solution as the length can't be negative.

The lengths of the sides are:
9 cm and 12 cm.

Check:

{{{15^2 = 9^2 + (9+3)^2}}}
{{{225 = 81 + 144}}}
{{{225 = 225}}}