Question

which set of side lengths can form a triangle? 4 meters, 11 meters, 19 meters 7 meters, 11 meters, 19 meters 4 meters, 17 meters, 22 meters 7 meters, 17 meters, 22 meters

Explanation:

To determine if a set of side lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side.

Step 1: Check the first set (4, 11, 19)

• \(4 + 11 = 15\), and \(15 < 19\). So, this set does not satisfy the triangle inequality.

Step 2: Check the second set (7, 11, 19)

• \(7 + 11 = 18\), and \(18 < 19\). So, this set does not satisfy the triangle inequality.

Step 3: Check the third set (4, 17, 22)

• \(4 + 17 = 21\), and \(21 < 22\). So, this set does not satisfy the triangle inequality.

Step 4: Check the fourth set (7, 17, 22)

• \(7 + 17 = 24\), and \(24 > 22\)
• \(7 + 22 = 29\), and \(29 > 17\)
• \(17 + 22 = 39\), and \(39 > 7\)

All three conditions of the triangle inequality are satisfied for this set.

Answer:

7 meters, 17 meters, 22 meters