Answer:
See Explanation
Step-by-step explanation:
Sample Response: No, the triangle is not possible. The triangle inequality rule states the sum of any two sides must be greater than the third side. 6 + 4 is 10, which is less than 11.
Garry construct a triangle with segments that are 4,6, and 11 inches long is not possible as it does not follow the triangle inequality rule.
The sides of triangle by which the Garry wants to construct a triangle are 4,6 and 11 in.
To find out the possibility of the triangle with the given sides can be verify using the triangle inequality rule.
Triangle inequality rule states that in any triangle the sum of the any two sides must be greater than the third side of the triangle. Let a, b and c are the sides of triangle then according to the triangle inequality rule,
[tex]a+b>c[/tex]
[tex]a+c>b[/tex]
[tex]b+c>a[/tex]
Now in the question given apply the triangle inequity rule to find out the possibility to construct such triangle,
[tex]6+11>4[/tex]
[tex]11+4>6[/tex]
But,
[tex]4+6<11[/tex]
Hence, to construct a triangle with segments that are 4,6, and 11 inches long is not possible as it does not follow the triangle inequality rule.
For more about the triangle inequality rule follow the link below-
https://brainly.com/question/9642592
