Question

determine which value is possible for x. (1 point)

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, \(x + 17>21\), \(x+21 > 17\) (which is always true for positive \(x\)), and \(17 + 21>x\).
From \(x + 17>21\), we get \(x>21 - 17\), so \(x>4\). From \(17 + 21>x\), we get \(x<38\).

Step2: Check the options

We check the given options against the inequality \(4 < x<38\).

• For \(x = 47\), \(47>38\), not valid.
• For \(x = 27\), \(4<27<38\), valid.
• For \(x = 38\), \(x = 38\) does not satisfy \(x<38\), not valid.
• For \(x = 4\), \(x = 4\) does not satisfy \(x>4\), not valid.

Answer:

27