Question

a triangle has two sides of length 17.4 and 12.6. what compound inequality describes the possible lengths for the third side, x? write a compound inequality like 1 < x < 3.

Explanation:

Step1: Calculate the difference of the two given sides

The difference of \(17.4\) and \(12.6\) is \(17.4 - 12.6=4.8\).

Step2: Calculate the sum of the two given sides

The sum of \(17.4\) and \(12.6\) is \(17.4 + 12.6 = 30\).

Step3: Apply the triangle - side - length relationship

For a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Here \(a = 17.4\), \(b=12.6\), so \(4.8\lt x\lt30\).

Answer:

\(4.8\lt x\lt30\)