This question is quite intriguing. At first glance, you might say it's quite trivial. All you have to do get a map and a ruler and sit down and measure it. The only problem with it is finding the time to do it. But is it that simple as that?
If you measure the coastline with a map using a large scale, you have a great estimate of the length. But what if you actually went to the coastline and measured it directly? Again, you might have a more accurate calculation than with a map but the measurement will still be a great estimate.
It will turn out that the smaller the scale, the estimate length will start increasing without limit! Therefore, hypothetically, if the scale of measurement decreases, for example infinitely small, then the estimate length would become infinitely large!
Then to answer the question, the coastline of British Columbia is infinitely long?? Does that make sense. If you were to measure all the little nooks and crannies on the coast and every point so that you have increased the resolution, wouldn't the measurement be infinite in length?
This is what a fractal is.
It is said it has dimensions between 1 and 2. This is because a one-dimension figure is a line. The coastline is not quite a line. However, it's not really a two-dimensional object either since this coastline at infinite magnification doesn't cover over a plane. So that is why it is said to be between 1 and 2. Some have speculated that it could be 1.2 but the calculations is far beyond basic comprehension.