Question

two sides of an acute - triangle measure 5 inches and 8 inches. the length of the longest side is unknown. what is the greatest possible whole - number length of the unknown side? 8 inches 9 inches 12 inches 13 inches

Explanation:

Step1: Recall triangle - side length rules

For any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let the sides of the triangle be \(a = 5\) inches, \(b = 8\) inches, and the unknown side be \(c\). If \(c\) is the longest side, then \(a + b>c\), i.e., \(c<5 + 8=13\) inches.

Step2: Consider the nature of whole - number values

Since \(c\) is a whole - number and we want the greatest possible value for \(c\) while still satisfying the triangle inequality, and \(c<13\), the greatest whole - number value for \(c\) is 12 inches.

Answer:

12 inches