Holly has a rectangular garden that measures 12 m wide by 14 m long. she wants to increase the area to 255 m² by increasing the width and length by the same amount.

what will be the length (longer dimension) of the new garden?

Present area = 12 * 14 = 168 square meters
The area has to increase by a factor of 255 / 168 = 1.5178571429
Therefore, the width and length are increased by a factor of the
square root of 1.5178571429 = 1.2320134508

So the width becomes
12 * 1.2320134508 =  14.7841614091
and the length becomes
14 * 1.2320134508 =  17.2481883107

That's roughly 14.78 by 17.25 and the area equals
14.78 * 17.25 = 255 square meters