Question

determine which set of side measurements could be used to form a triangle. 13, 19, 7 25, 12, 13 18, 2, 24 3, 1, 5

Explanation:

Step1: Check the triangle inequality for 13, 19, 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 \(a = 7\), \(b = 13\), \(c = 19\):
\(7+13 = 20>19\), \(7 + 19=26>13\), \(13+19 = 32>7\)

Step2: Check the triangle inequality for 25, 12, 13

For \(a = 12\), \(b = 13\), \(c = 25\):
\(12 + 13=25
ot>25\)

Step3: Check the triangle inequality for 18, 2, 24

For \(a = 2\), \(b = 18\), \(c = 24\):
\(2+18 = 20
ot>24\)

Step4: Check the triangle inequality for 3, 1, 5

For \(a = 1\), \(b = 3\), \(c = 5\):
\(1+3=4
ot>5\)

Answer:

13, 19, 7