Question

select the correct answer. based on these 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 \(a\), \(b\), \(c\) (where \(c\) is the largest), the sum of any two sides must be greater than the third side, i.e., \(a + b>c\), \(a + c>b\), \(b + c>a\). Simplified, we check if the sum of the two smaller sides is greater than the largest side.

Step2: Check Option A (3, 10, 14)

Largest side is 14. Sum of smaller sides: \(3 + 10 = 13\). Since \(13<14\), does not satisfy.

Step3: Check Option B (8, 7, 13)

Largest side is 13. Sum of smaller sides: \(7 + 8 = 15\). Since \(15>13\), check other inequalities ( \(7 + 13>8\) and \(8 + 13>7\), which are true). So this satisfies.

Step4: Check Option C (3, 2, 5)

Largest side is 5. Sum of smaller sides: \(2 + 3 = 5\). Since \(5 = 5\) (not greater), does not satisfy.

Step5: Check Option D (20, 7, 13)

Largest side is 20. Sum of smaller sides: \(7 + 13 = 20\). Since \(20 = 20\) (not greater), does not satisfy.

Answer:

B. 8, 7, 13