A second ant walks all the way around a triangle drawn in the dirt. Two of the dimensions of the triangle are 5 1/10 centimeters and 7 1/5 centimeters. The total distance traveled by the ant is 20 centimeters. What is the length of the third side of triangle?
Let's assume that the third side of the triangle has a length of x centimeters.
The ant walks around the triangle, so it covers the distance of all three sides.
The distance traveled by the ant on the first side is 5 1/10 centimeters.
The distance traveled by the ant on the second side is 7 1/5 centimeters.
The distance traveled by the ant on the third side is x centimeters.
The total distance traveled by the ant is the sum of the distances on each side, so 5 1/10 + 7 1/5 + x = 20.
To simplify the equation, let's turn the mixed numbers into improper fractions: 5 1/10 = 51/10 and 7 1/5 = 36/5.
So the equation becomes: 51/10 + 36/5 + x = 20.
To get rid of the denominators, we can multiply every term in the equation by 10: 10(51/10) + 10(36/5) + 10(x) = 10(20).
This simplifies to: 51 + 72 + 10x = 200.
Combining like terms: 123 + 10x = 200.
Subtracting 123 from both sides: 123 - 123 + 10x = 200 - 123.
This simplifies to: 10x = 77.
Dividing both sides by 10: 10x/10 = 77/10.
This simplifies to: x = 77/10.
In decimal form, x is approximately equal to 7.7 centimeters.
Therefore, the length of the third side of the triangle is 7.7 centimeters. Answer: \boxed{7.7}.