Final answer:
The length of the longest bar is 1 7/12 feet.
Step-by-step explanation:
To find the length of the longest bar, we need to compare the given lengths. The lengths are 1.75 feet, 1 7/12 feet, and 1 2/3 feet. We can convert the mixed numbers to improper fractions for ease of comparison. The lengths in improper fraction form are 1.75 feet = 1 3/4 feet, 1 7/12 feet remains the same, and 1 2/3 feet = 1 2/3 feet.
Now, we can find the common denominator of the fractions, which is 12. The lengths in fractions with a common denominator are 1 3/4 feet = 7/4 feet, 1 7/12 feet = 19/12 feet, and 1 2/3 feet = 5/3 feet.
Comparing the fractions, we can see that 19/12 is the largest. Therefore, the longest bar is 1 7/12 feet.