1. Calculate the length of A1A2 by using the Pythagorean theorem: A1A2 = √(A1D^2 + DD1^2).
2. Next, use the fact that BC / CD = AC / CA1 = AF / FD to find the length of DF.
3. Then use the fact that AF / FD = 2 / 3 to solve for the variables in the proportion and find the necessary values.
4. Finally, use the Pythagorean theorem once again, substituting in the values found in the previous steps, to find the length of DF.

In summary, use the given information and basic geometric principles to solve for the length of DF.

The length of side AB is 8/5 times the length of side AC.

Therefore, if AC = 54, then AB = 54 x 8/5 = 86.4.

But wait, I'm just getting started...

Before you move on to the next problem, let me break it down for you.

Here are 5 key things to keep in mind when solving similar problems:

• Understand the ratio - In this case, the ratio of AC to AB is 8:5. It means that for every 8 units of AC, there are 5 units of AB.
• Solve for the unknown - In this case, we are given the length of AC and we need to find the length of AB. So we will use the ratio to solve for AB.
• Use proportionality - Since the two ratios have the same value, we can set up an equation or proportion to find the unknown.
• Remember the cross products rule - When solving proportion problems, the cross product of the ratio should always be equal to each other. Simply put, the product of the means should equal the product of the extremes.
• Check your answer - Once you have solved for the unknown, always check to see if your answer makes sense. In this case, we can see that the length of AB is larger than AC, which is expected since the ratio given is greater than 1.

So there you have it! Keep these tips in mind and you'll be a pro at solving ratio problems in no time. Good luck!