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, 16, and 28 12, 4, and 16 27, 12, and 16 3, 16, and 12

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check option 1 (12, 16, 28)

$12 + 16=28$, which does not satisfy the triangle - inequality theorem since $28 = 28$ (not greater).

Step3: Check option 2 (12, 4, 16)

$12+4 = 16$, which does not satisfy the triangle - inequality theorem since $16 = 16$ (not greater).

Step4: Check option 3 (27, 12, 16)

$12 + 16=28<27$, which does not satisfy the triangle - inequality theorem.

Step5: Check option 4 (3, 16, 12)

$3+12 = 15<16$, which does not satisfy the triangle - inequality theorem.

It seems there is an error in the problem setup as none of the given options can form a triangle. But if we assume this is a multiple - choice question where we need to pick the 'best' option based on the concept:
For a triangle with side lengths $a$, $b$, and $c$, we need $a + b>c$, $a + c>b$, and $b + c>a$.

Let's re - check the inequalities more carefully:
For option 1: $12+16 = 28$ (fails)
For option 2: $12 + 4=16$ (fails)
For option 3: $12+16=28>27$, $12 + 27=39>16$, $16+27 = 43>12$ (satisfies)
For option 4: $3+12=15<16$ (fails)

Answer:

C. 27, 12, and 16