The length of the original side of the garage is √318 = 17.8 feet
50% more floor space means the garage is now 318 x 1.5 = 477 ft^2, the length of the new side would be √477 = 21.8 ft ^2
The percent increase is found by finding the difference and dividing it by the original:
21.8 - 17.8 = 4 feet
4 / 17.8 = 0.2247 = 22.5% increase