For a craft project, four students each chose three pieces of wire from a box.


Don’s wires measure 3 inches, 5 inches, and 12 inches.

Margo’s wires measure 6 inches, 8 inches, and 14 inches.

Sonji’s wires measure 12 inches, 8 inches, and 17 inches.

Liam’s wires measure 16 inches, 8 inches, and 27 inches.


Which student chose pieces that can be used to construct a triangle?


Don

Margo

Sonji

Liam

Respuesta :

Answer:

Sonji

Step-by-step explanation:

To find the answer, we need to recur to the triangular inequality, which states that the sum of two sides must be greater than the third side

[tex]a+b>c[/tex]

So, if we apply this triangular inequality to each case, we would find that Sonji's wires can make a triangle, because

[tex]12+8 > 17\\20 > 17[/tex]

Fulfils the theorem.

On the other hand, we have the other measures

Don:

[tex]3+5 > 12\\8 > 12[/tex]

Which is false.

Margo:

[tex]6+8>14\\14>14[/tex]

Which is also false.

Liam

[tex]16+8>27\\24>17[/tex]

False again.

Therefore the right answer is Sonji.

Answer: Option 3 or C. Sonji’s wires measure 12 inches, 8 inches, and 17 inches.

Step-by-step explanation:  Trust Me!

I took the quiz and got 100% correct on Edge 2022. If you are working on Edge the answer is correct. The proof is down below.

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