Question

find the range of values for the third side of a triangle if two of its sides measure 42.7 mm and 38.03 mm. (1 point)

$4.67 < x < 80.73$

$4.4 < x < 80.73$

$4.67 < x < 42.3$

$4.04 < x < 80.1$

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies the inequalities \(|a - b|\lt x\lt a + b\).

Step2: Calculate the difference

Let \(a = 42.7\) mm and \(b = 38.03\) mm. Then \(|a - b|=|42.7-38.03| = 4.67\) mm.

Step3: Calculate the sum

\(a + b=42.7 + 38.03=80.73\) mm.

Answer:

A. \(4.67 < x < 80.73\)