Question

mr romero has several boards of differing lengths to construct a triangle. he will use two boards already cut and sanded to lengths of 23 inches and 14 inches. between which two numbers must the third side be cut to length? support your claim and draw a diagram.

Explanation:

Step1: Apply the triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(|a - b|\lt c\lt a + b\). Let \(a = 23\) inches and \(b=14\) inches.
First, calculate \(a - b\): \(23-14 = 9\).

Step2: Calculate \(a + b\)

Next, calculate \(a + b\): \(23 + 14=37\).

Answer:

The length of the third side must be greater than \(9\) inches and less than \(37\) inches. So the third side \(x\) satisfies \(9\lt x\lt37\).