Question

sides of a triangle quick check a triangle’s side lengths are whole numbers. if the measure of two of its sides are 1 cm and 13 cm, what is the measure of the third side? (1 point) 12 cm 13 cm 1 cm 12.5 cm

Explanation:

Step1: Recall triangle inequality theorem

For a triangle with sides \(a\), \(b\), \(c\), the inequalities are \(|a - b| < c < a + b\). Here, \(a = 1\), \(b = 13\). So \(|13 - 1| < c < 13 + 1\), which simplifies to \(12 < c < 14\).

Step2: Check whole number and options

The third side \(c\) must be a whole number. Among options, only \(13\) satisfies \(12 < 13 < 14\). \(12\) is not greater than \(12\), \(1\) is too small, \(12.5\) is not a whole number.

Answer:

B. 13 cm