Question

a triangle has two sides measuring 8.5 cm and 15 cm. what is the greatest whole number length possible for the third side? explain
a. 23; the third side length must be greater than 8.5 + 15 = 23.5. the smallest whole number greater than 23.5 is 23.
b. 24; the third side length must be less than 8.5 + 15 = 23.5. the greatest whole number less than 23.5 is 24.
c. 23; the third side length must be less than 8.5 + 15 = 23.5. the greatest whole number less than 23.5 is 23
d. 24; the third side length must be greater than 8.5 + 15 = 23.5. the smallest whole number greater than 23.5 is 24

Explanation:

Step1: Apply triangle inequality theorem

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let the two given sides be \(a = 8.5\) cm and \(b=15\) cm, and the third side be \(c\). Then \(c\lt a + b\).

Step2: Calculate \(a + b\)

\(a + b=8.5+15 = 23.5\) cm.

Step3: Find the greatest whole - number less than \(23.5\)

The greatest whole number \(n\) such that \(n\lt23.5\) is \(n = 23\)

Answer:

C. 23, the third side length must be less than \(8.5 + 15=23.5\). The greatest whole number less than \(23.5\) is 23