Question 100465
Let the original side length be x.Then,
{{{(x+5)^2 = 289}}} Solve for x.
{{{x^2+10x+25 = 289}}} Subtract 289 from both sides.
{{{x^2+10x-264 = 0}}} Solve this quadratic equation for x by factoring.
{{{(x-12)(x+22) = 0}}}
{{{x-12 = 0}}} so {{{x = 12}}} or
{{{x+22 = 0}}} so {{{x = -22}}} Discard the negative solution as the side length is a positive value.
The original side length is 12 cm.

Check:
{{{(x+5)^2 = (12+5)^2}}}
{{{17^2 = 289}}}