Question

can the sides of a triangle have lengths 6, 10, and 13?
yes
no

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.

Step2: Check first combination

Check if \(6 + 10>13\).
\(6 + 10=16\) and \(16>13\).

Step3: Check second combination

Check if \(6+13 > 10\).
\(6 + 13=19\) and \(19>10\).

Step4: Check third combination

Check if \(10 + 13>6\).
\(10+13 = 23\) and \(23>6\).

Answer:

yes