The measure of two sides of a triangle are 5.2 and 8.1. determine the range of values for the third side of the triangle. (1 point)
___ < n < ___
To find the range of values for the third side of the triangle, we can use the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, in this case, we can set up the following inequality:
5.2 + 8.1 > n
13.3 > n
Therefore, the minimum value for the third side (n) is 13.3.
For the maximum value, we can use the other side length:
8.1 + 8.1 > n
16.2 > n
Therefore, the maximum value for the third side (n) is 16.2.
So, the range of values for the third side of the triangle is:
13.3 < n < 16.2.
Sorry. That was not the correct answer.
Apologies for the incorrect answer. Let's try again.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, to find the range of values for the third side of the triangle, we need to consider the possible combinations of the given side lengths.
Let's label the sides of the triangle as follows:
Side 1: 5.2
Side 2: 8.1
Side 3: n (unknown)
Case 1: Side 3 is the largest side
In this case, Side 3 must be greater than the difference between Side 1 and Side 2:
n > 8.1 - 5.2
n > 2.9
Case 2: Side 1 is the largest side
In this case, Side 1 (5.2) must be greater than the difference between Side 2 and Side 3:
5.2 > 8.1 - n
n > 2.9
Therefore, the range of values for the third side (n) of the triangle is:
2.9 < n
Now, the other space.
Apologies for the oversight. Let's consider the other case:
Case 3: Side 2 is the largest side
In this case, Side 2 (8.1) must be greater than the difference between Side 1 and Side 3:
8.1 > 5.2 - n
n < 2.9
Therefore, the range of values for the third side (n) of the triangle is:
2.9 < n < 8.1.
To summarize, the correct range of values for the third side of the triangle is:
2.9 < n < 8.1.
Sorry. That was not the correct answer for that space.
Apologies for the previous incorrect response. Let's try again.
To determine the range of values for the third side of the triangle, we need to consider the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's label the sides of the triangle as follows:
Side 1: 5.2
Side 2: 8.1
Side 3: n (unknown)
For the minimum value, we consider the case where Side 3 is the greatest side. In this case, the sum of Side 1 and Side 2 must be greater than Side 3:
5.2 + 8.1 > n
13.3 > n
So, the minimum value for the third side (n) is 13.3.
For the maximum value, we consider the case where Side 3 is the smallest side. In this case, the difference between Side 2 and Side 1 must be less than Side 3:
8.1 - 5.2 < n
2.9 < n
So, the maximum value for the third side (n) is 2.9.
Therefore, the range of values for the third side of the triangle is:
2.9 < n < 13.3.