Question

iliana claims that she can construct a triangle from a 12 - inch rod, a 36 - inch rod, and a 30.4 - inch rod. which statement explains whether she is correct?
iliana will be able to construct a triangle because the sum of any two sides is less than the third side.
iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side.
iliana cannot construct a triangle because the sum of the two smaller sides will be greater than the third side.
iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.

Explanation:

Step1: Find the sum of the two smaller sides

The two smaller sides are \(12\) - inch and \(30.4\) - inch.
\(12 + 30.4=42.4\)

Step2: Compare the sum with the largest side

The largest side is \(36\) - inch.
Since \(42.4>36\)

Answer:

Iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.