Question

1. which of the following could not be the lengths of the three sides of a triangle?

3 millimeters, 6 millimeters, 9 millimeters
4 yards, 6 yards, 8 yards
5 centimeters, 12 centimeters, 13 centimeters
3 inches, 4 inches, 5 inches

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (where \(a\leq b\leq c\)), the sum of the two shorter sides must be greater than the longest side (\(a + b>c\)).

Step2: Check each option

• Option 1: \(3\) mm, \(6\) mm, \(9\) mm

Let \(a = 3\), \(b = 6\), \(c=9\). Then \(a + b=3 + 6=9\), and \(9
ot>9\) (since \(a + b=c\)).

• Option 2: \(4\) yards, \(6\) yards, \(8\) yards

Let \(a = 4\), \(b = 6\), \(c = 8\). Then \(a + b=4+6 = 10>8\).

• Option 3: \(5\) cm, \(12\) cm, \(13\) cm

Let \(a = 5\), \(b = 12\), \(c = 13\). Then \(a + b=5 + 12=17>13\).

• Option 4: \(3\) inches, \(4\) inches, \(5\) inches

Let \(a = 3\), \(b = 4\), \(c = 5\). Then \(a + b=3+4 = 7>5\).

Answer:

3 millimeters, 6 millimeters, 9 millimeters