Question

based on the segment lengths, which group of segments can form a triangle?
a. 3, 10, 14
b. 8, 7, 13
c. 3, 2, 5
d. 20, 7, 13

Explanation:

Step1: Recall triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the sum of the two shorter sides \(a + b>c\)

Step2: Check option A

\(a = 3\), \(b = 10\), \(c = 14\). Then \(a + b=3 + 10=13<14\)

Step3: Check option B

\(a = 7\), \(b = 8\), \(c = 13\). Then \(a + b=7 + 8 = 15>13\)

Step4: Check option C

\(a = 2\), \(b = 3\), \(c = 5\). Then \(a + b=2+3 = 5
ot>5\)

Step5: Check option D

\(a = 7\), \(b = 13\), \(c = 20\). Then \(a + b=7 + 13=20
ot>20\)

Answer:

B. 8, 7, 13