Question

alisha wants to build a miniature bridge that will include a triangle made of wooden pieces. which lengths of wood can she use to form a triangle? all lengths are given in inches. (1 point)
○ 12, 4, and 16
○ 3, 16, and 12
○ 12, 16, and 28
○ 27, 12, and 16

Explanation:

Step1: Recall Triangle Inequality Theorem

For three lengths \(a\), \(b\), \(c\) to form a triangle, the sum of any two sides must be greater than the third side: \(a + b>c\), \(a + c>b\), \(b + c>a\).

Step2: Check Option 1: 12, 4, 16

Check \(12 + 4\) vs \(16\): \(12 + 4 = 16\), but \(16\) is not greater than \(16\) (needs to be \(>\)), so invalid.

Step3: Check Option 2: 3, 16, 12

Check \(3 + 12\) vs \(16\): \(3+12 = 15<16\), so invalid.

Step4: Check Option 3: 12, 16, 28

Check \(12 + 16\) vs \(28\): \(12 + 16 = 28\), not greater, invalid.

Step5: Check Option 4: 27, 12, 16

Check \(12 + 16 = 28>27\), \(12 + 27 = 39>16\), \(16 + 27 = 43>12\). All inequalities hold.

Answer:

27, 12, and 16 (the last option)