Question

applications of constructions quick check
if a triangle has sides of 31 in. and 28 in., which is a possible length for the third side? (1 point)
3 in.
33 in.
62 in.
59 in.

Explanation:

Step1: Recall 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, and the difference between the lengths of any two sides must be less than the length of the third side. Let the sides of the triangle be \(a = 31\) in, \(b = 28\) in, and \(c\) be the third - side. Then \(|a - b|\lt c\lt a + b\).

Step2: Calculate the lower and upper bounds

First, calculate \(a - b\): \(31-28 = 3\) in. Then calculate \(a + b\): \(31 + 28=59\) in. So, \(3\lt c\lt59\).

Answer:

B. 33 in