Select the correct answer.
A triangle has one side of length 29 units and another of length 40 units. Determine the range in which the length of the third side must lie.
A.
-11< x < 69
B.
11≤ x ≤ 69
C.
11< x < 69
D.
-11≤ x ≤ 69
To determine the range in which the length of the third side of the triangle must lie, 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.
Let's denote the length of the third side as "x". Given that one side of length is 29 units and another is 40 units, we can write the following inequality:
29 + 40 > x
Simplifying the inequality:
69 > x
Therefore, the correct answer is:
C. 11< x < 69
To determine the range in which the length of the third side must lie, we can use the triangle inequality theorem. According to the theorem, 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 known sides have lengths of 29 and 40 units. Therefore, the range for the length of the third side (x) can be found by setting up the following inequality:
29 + 40 > x
Simplifying, we have:
69 > x
Therefore, the range for the length of the third side must be x > 11.
The correct answer is:
C.
11 < x < 69
To determine the range in which the length of the third side of the triangle must lie, 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.
Let's denote the length of the third side as "x". In this case, the given side lengths are 29 and 40 units.
Using the triangle inequality theorem, we can write two inequalities:
1. 29 + x > 40 (by adding the smallest side to x, the third side)
2. 40 + x > 29 (by adding the other side to x, the third side)
Simplifying these inequalities, we get:
1. x > 11
2. x > -11
Since the length of a side cannot be negative in this context, we can conclude that x must be greater than 11. Hence, the correct answer is C.
Therefore, the range in which the length of the third side must lie is 11 < x < 69.