Question

1. can a triangle with sides 3, 7, and 13 be formed? why or why not?
2. what is the minimum and maximum (the range) that the missing side can be?

Explanation:

Step1: Check triangle inequality for question 1

Triangle inequality: sum of two sides > third side.
For sides \(3\), \(7\), \(13\):
\(3 + 7=10<13\).

Step2: Apply triangle inequality for question 2

Let the sides be \(6\) and \(11\). Let the missing side be \(x\).
By triangle inequality: \(|a - b|Here \(a = 11\), \(b = 6\).
\(11-6\(5

Answer:

1. No, because \(3 + 7<13\) (violates triangle - inequality).
2. The minimum value (lower - bound, not inclusive) of the missing side is \(5\) and the maximum value (upper - bound, not inclusive) is \(17\). So the range is \(5