a second ant walks all the way around a traingle 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 the triangle

Answer 1

To find the length of the third side of the triangle, you can apply the concept known as the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Let's denote the length of the third side as x. The two given sides are 5 1/10 centimeters and 7 1/5 centimeters, which can be converted to improper fractions as follows:

5 1/10 = (50 + 1)/10 = 51/10
7 1/5 = (70 + 1)/5 = 71/5

So, applying the triangle inequality theorem, we have:

x < 51/10 + 71/5

To simplify the right-hand side of the equation, we need a common denominator, which is 10 in this case:

x < (51 + 142)/10
x < 193/10

Thus, the length of the third side is less than 19 3/10 centimeters.

Note: The triangle inequality theorem does not give an exact value for the third side; it only provides an upper limit. To find the exact value, additional information or measurements would be needed.