The problem asks whether a triangle can have sides of length 4, 12, and 18.

1. Problem Description

The problem asks whether a triangle can have sides of length 4, 12, and

1

8.

2. Solution Steps

To determine if a triangle can be formed with sides of lengths $a$, $b$, and $c$, the triangle inequality must hold. This means the sum of any two sides must be greater than the third side. In other words:

$a + b > c$

$a + c > b$

$b + c > a$

In this case, $a=4$, $b=12$, and $c=18$. We need to check if the three inequalities hold:

$4 + 12 > 18 \Rightarrow 16 > 18$, which is false.

$4 + 18 > 12 \Rightarrow 22 > 12$, which is true.

$12 + 18 > 4 \Rightarrow 30 > 4$, which is true.

Since one of the inequalities ($4 + 12 > 18$) is false, the triangle inequality is not satisfied. Therefore, a triangle cannot be formed with sides of length 4, 12, and

1

8.

3. Final Answer

No