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
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.
To find the length of the third side of the triangle, we can start by subtracting the lengths of the two given sides from the total distance traveled by the ant.
Given sides:
Side 1: 5 1/10 centimeters
Side 2: 7 1/5 centimeters
Total distance traveled: 20 centimeters
Subtracting the lengths of the given sides from the total distance:
20 cm - (5 1/10 cm + 7 1/5 cm)
To subtract the mixed numbers, we need to find a common denominator. The least common multiple (LCM) of 10 and 5 is 10.
Convert 5 1/10 cm to an improper fraction: 5 1/10 = 51/10 cm
Convert 7 1/5 cm to an improper fraction: 7 1/5 = 36/5 cm
Now, we can rewrite the subtraction:
20 cm - (51/10 cm + 36/5 cm)
Next, let's convert the fractions to have a common denominator of 10:
20 cm - (51/10 cm + (36/5 cm * 2/2))
20 cm - (51/10 cm + 72/10 cm)
Combining the fractions:
20 cm - (51/10 cm + 72/10 cm)
20 cm - (123/10 cm)
To subtract fractions, we need a common denominator of 10:
20 cm * 10/10 - (123/10 cm)
200/10 cm - 123/10 cm
Now, subtract the fractions:
(200 - 123)/10 cm
77/10 cm
Therefore, the length of the third side of the triangle is 77/10 centimeters or 7 7/10 centimeters.