Answer:
If s₃ is the length of the 3rd side, the possible values are in the interval.
5 < s₃ < 19
Explanation:
For a triangle, we know that the sum of any two sides is always larger than the other side.
So if a triangle has 3 sides:
s₁, s₂, and s₃, we have:
s₁ + s₂ > s₃
s₁ + s₃ > s₂
s₂ + s₃ > s₁
In this case, we know that two sides are:
s₁ = 7
s₂ = 12
And we want to find the possible values of s₃.
Then if we use the above inequalities, we get:
7 + 12 > s₃
7 + s₃ > 12
12 + s₃ > 7
With the first one we get:
19 > s₃
Now we can rewrite the other two as:
s₃ > 12 - 7 = 5
s₃ > 7 - 12 = -5
The first one is more restrictive than the second:
s₃ > 5 > -5
So we can use only the first one.
Then the two inequalities are
s₃ > 5
s₃ < 19
Then the range is:
5 < s₃ < 19
This means that any value between 5 and 19 can be a possible length of the third side (5 and 19 are not possible lengths)