The measure of two sides of a triangle are 7 and 11. Determine the range of values for the third side of the triangle. (1 point)
< n <
To determine the range of values for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides of the triangle are 7 and 11. Let's call the third side x.
According to the triangle inequality theorem, we have the following inequality:
7 + 11 > x
Simplifying this inequality, we get:
18 > x
Therefore, the range of values for the third side of the triangle is:
0 < x < 18
Thus, the answer is:
< n < 18
what the number in the left
Apologies for the confusion. There is no specific number on the left side of the inequality. The correct range for the third side of the triangle is simply:
0 < x < 18
its wrong tho
Apologies for the previous incorrect response. To determine the range of values for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides of the triangle are 7 and 11. Let's call the third side x.
According to the triangle inequality theorem, we have the following inequality:
|x - 7| < 11
To find the range of values for x, we can split the inequality into two cases:
Case 1: x - 7 > 0
In this case, the inequality becomes:
x - 7 < 11
Simplifying:
x < 18
Case 2: x - 7 < 0
In this case, the inequality becomes:
-(x - 7) < 11
Simplifying:
7 - x < 11
- x < 11 - 7
- x < 4
Multiplying both sides by -1 and flipping the inequality sign:
x > -4
Combining the two cases, we have the range of values for x:
-4 < x < 18
Thus, the correct range of values for the third side of the triangle is:
-4 < x < 18
wrong again
Apologies for the incorrect response earlier.
To determine the range of values for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides of the triangle are 7 and 11. Let's call the third side x.
According to the triangle inequality theorem, we have the following inequalities:
x + 7 > 11 (the third side plus the shorter side must be greater than the longer side)
x + 11 > 7 (the third side plus the longer side must be greater than the shorter side)
Simplifying these inequalities:
x > 4
x > -4
Therefore, the range of values for the third side of the triangle is:
x > 4
Thus, the answer is:
x > 4.