Question

a triangle has side lengths 12 cm, 3 cm, and x cm. which measurement is not in the range of possible values of x?
9 cm
11 cm
13 cm

Explanation:

Step1: Apply triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, \(12 + 3>x\) (i.e., \(x < 15\)) and \(12+x>3\) (always true for positive \(x\)) and \(3 + x>12\), which gives \(x>9\).

Step2: Determine the range of \(x\)

The range of \(x\) is \(9 < x<15\).

Answer:

9 cm