Question

can the sides of a triangle have lengths 2, 12, and 12?
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 the three inequalities

1. Check \(2 + 12>12\).

• Calculate \(2 + 12=14\), and \(14>12\).

1. Check \(12 + 12>2\).

• Calculate \(12+12 = 24\), and \(24>2\).

1. Check \(2+12>12\) (already done in the first - check).

Since all three inequalities hold true, the sides with lengths 2, 12, and 12 can form a triangle.

Answer:

yes