Question

choose possible values of x. 12 13 15 9 11

Explanation:

Step1: Apply triangle - inequality theorem

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let the sides of the triangle be \(8\), \(x\), and \(20\). So we have three inequalities: \(8 + x>20\), \(8 + 20>x\), and \(x + 20>8\) (the third one is always true for non - negative \(x\)).
From \(8 + x>20\), we get \(x>20 - 8\), so \(x>12\). From \(8+20 > x\), we get \(x<28\).

Step2: Check the options

We check each option against the inequality \(12 < x<28\).

• For \(x = 12\), it does not satisfy \(x>12\).
• For \(x = 13\), since \(12<13<28\), it is a valid value.
• For \(x = 15\), since \(12<15<28\), it is a valid value.
• For \(x = 9\), it does not satisfy \(x>12\).
• For \(x = 11\), it does not satisfy \(x>12\).

Answer:

13, 15