Question

1. do the following side lengths form a triangle? 4, 10, 7

a) yes b) no

1. do the following side lengths form a triangle? 5, 5, 10

a) yes b) no

1. do the following side lengths form a triangle? 13, 5, 6

a) yes b) no

Explanation:

Step1: Check triangle inequality for 4,10,7

The triangle inequality states that for any triangle with side lengths \(a\), \(b\), \(c\), \(a + b>c\), \(a + c>b\), and \(b + c>a\).
For \(a = 4\), \(b = 7\), \(c = 10\):
\(4+7 = 11>10\), \(4 + 10=14>7\), \(7+10 = 17>4\)

Step2: Check triangle inequality for 5,5,10

For \(a = 5\), \(b = 5\), \(c = 10\):
\(5+5=10
ot> 10\)

Step3: Check triangle inequality for 13,5,6

For \(a = 5\), \(b = 6\), \(c = 13\):
\(5+6=11
ot>13\)

Answer:

1. a) Yes
2. b) No
3. b) No