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 must lie, 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.
Let the length of the third side be x units. According to the triangle inequality theorem:
29 + 40 > x
69 > x
Therefore, x must be less than 69 units.
40 + x > 29
x > -11
Therefore, x must be greater than -11 units.
Combining these results, the range in which the length of the third side must lie is -11 < x < 69.
The correct option is A. -11 < x < 69.
I think you mean C, since angles are not negative
40-29 < x < 40+29
11 < x < 69