Question

name: unit 5: relationships in triangles date: bell: homework 6: triangle inequalities this is a 2 - page document! directions: determine if the side lengths could form a triangle. use an inequality to prove your answer. 1. 16 m, 21 m, 39 m 2. 18 in, 6 in, 13 in 3. 34 km, 27 km, 58 km 4. 29 ft, 38 ft, 9 ft 5. 12 cm, 12 cm, 25 cm 6. 31 yd, 14 yd, 19 yd

Explanation:

Problem 1: 16 m, 21 m, 39 m

Step1: Recall Triangle Inequality Theorem

The sum of any two sides of a triangle must be greater than the third side. So we check \(16 + 21\), \(16+39\), and \(21 + 39\) against the third side.

Step2: Check \(16 + 21\) vs \(39\)

Calculate \(16+21 = 37\). Now, compare \(37\) and \(39\). Since \(37<39\), the sum of the two smaller sides is not greater than the largest side.

Step1: Identify the sides

Let the sides be \(a = 6\), \(b = 13\), \(c = 18\) (order by length).

Step2: Check \(a + b\) vs \(c\)

Calculate \(6 + 13=19\). Compare \(19\) and \(18\). Since \(19>18\). Also check other sums: \(6 + 18=24>13\) and \(13 + 18 = 31>6\).

Step1: Order the sides

Let \(a = 27\), \(b = 34\), \(c = 58\).

Step2: Check \(a + b\) vs \(c\)

Calculate \(27+34 = 61\). Compare \(61\) and \(58\). Since \(61>58\). Other sums: \(27 + 58=85>34\) and \(34 + 58=92>27\).

Answer:

The side lengths \(16\) m, \(21\) m, \(39\) m cannot form a triangle.

Problem 2: 18 in, 6 in, 13 in