First, you want to add together the numbers in the extended ratio. 6 + 7 + 8 = 21. This helps because you're looking to find how much greater the triangle is than the ratio.
So now, since you have the total "perimeter" of a triangle with sides of that ratio, just divide 63 by 21 to find how many times that ratio fits into this triangle.
63 / 21 = 3
So you now know that if you multiply all the parts of that ratio by 3, it'll get the side lengths of the triangle with a perimeter of 63 feet.
6 * 3 : 7 * 3 : 8 * 3 = 18:21:24
So the side lengths would be 18 feet, 21 feet, and 24 feet.
To check, I would add all the sides together to see if it equals 63 feet:
