Question

1. which list shows three line segments that could not form a triangle?

a. 4cm, 7cm, 13cm
b. 5cm, 6cm, 7cm
c. 3cm, 6cm, 6cm
d. 6cm, 8cm, 10cm
1.

Explanation:

Step1: Check triangle inequality for option a

Triangle inequality: \(a + b>c\), \(a + c>b\), \(b + c>a\). For \(a = 4\), \(b = 7\), \(c = 13\), \(4+7=11<13\).

Step2: Check triangle inequality for option b

For \(a = 5\), \(b = 6\), \(c = 7\), \(5 + 6=11>7\), \(5+7 = 12>6\), \(6 + 7=13>5\).

Step3: Check triangle inequality for option c

For \(a = 3\), \(b = 6\), \(c = 6\), \(3+6=9>6\), \(3 + 6=9>6\), \(6+6=12>3\).

Step4: Check triangle inequality for option d

For \(a = 6\), \(b = 8\), \(c = 10\), \(6+8=14>10\), \(6 + 10=16>8\), \(8+10=18>6\).

Answer:

A. 4cm, 7cm, 13cm