Answer :
Explanation :
In order to determine the possible lengths of the 3rd side of the mentioned triangle,we can use the triangle inequality theorem which states that the sum of any of the two sides of a triangle must be greater than the third side .
thus, the sum of the possible length (x) of the third side and 11 must be greater than 18.
thus, any of the given values greater than 7 could be the possible length of the third side .
therefore,
option A,C,E, and F could be the possible length of the third side.
Answer:
A. 11
C. 8
E. 18
F. 28
Step-by-step explanation:
To determine the possible lengths of the third side of a triangle, we can use the triangle inequality theorem.
The theorem 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 a, b and c be the side lengths of a triangle.
According to the triangle inequality theorem:
[tex]a + b > c[/tex]
[tex]a + c > b[/tex]
[tex]b + c > a[/tex]
In this case, we have two side lengths given as 18 and 11.
Let a = 18 and b = 11:
[tex]18 + 11 > c[/tex]
[tex]18 + c > 11[/tex]
[tex]11 + c > 18[/tex]
Solving these inequalities will give us the possible lengths for the third side of the triangle.
[tex]\begin{aligned}18 + 11 & > c\\29& > c\\c& < 29\end{aligned}[/tex]
[tex]\begin{aligned}18 +c & > 11\\c& > 11-18\\c& > -7\end{aligned}[/tex]
[tex]\begin{aligned}11+c & > 18\\c& > 18-11\\c& > 7\end{aligned}[/tex]
Combining the results, we find that the possible lengths for the third side must be greater than 7 and less than 29.
Therefore, the possible lengths from the given answer options are:
