Complete the inequality so that it represents the whole number values that side a could be to create a triangle. The triangle measures are c=6 and b=5
A. 1<a<10
B. 0>a<10
C. 1<a<9
D. 1<a<11
In order for the lengths of sides a, b, and c to form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
For this triangle, c = 6 and b = 5. Let's assume the length of side a is x.
Using the triangle inequality theorem, we have:
x + 5 > 6
x > 1
and
x + 6 > 5
x > -1
Combining these inequalities, we get:
-1 < x < 1
Since we are looking for whole number values that side a could be, we can conclude that the possible values for side a are 0 and 1. Therefore, the complete inequality is:
0 < a < 1
The correct answer is not provided among the options.