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Can a triangle be formed with side lengths 6, 9, and 12? Explain.

A. No, because [tex]12 - 9 \ \textless \ 6[/tex]

B. Yes, because [tex]6 + 9 \ \textgreater \ 12[/tex]

C. Yes, because [tex]12 - 9 \ \textless \ 6[/tex]

D. No, because [tex]6 + 9 \ \textgreater \ 12[/tex]

Sagot :

GinnyAnsweridn
To determine whether a triangle can be formed using side lengths 6, 9, and 12, we must apply the triangle inequality theorem. This theorem states that for three side lengths to form a triangle, the sum of any two sides must be greater than the third side.

Let's check each condition:

1. First condition: The sum of the first side and the second side must be greater than the third side:
[tex]\[ 6 + 9 > 12 \][/tex]
Simplifying,
[tex]\[ 15 > 12 \][/tex]
This condition is true.

2. Second condition: The sum of the first side and the third side must be greater than the second side:
[tex]\[ 6 + 12 > 9 \][/tex]
Simplifying,
[tex]\[ 18 > 9 \][/tex]
This condition is true.

3. Third condition: The sum of the second side and the third side must be greater than the first side:
[tex]\[ 9 + 12 > 6 \][/tex]
Simplifying,
[tex]\[ 21 > 6 \][/tex]
This condition is true.

Since all three conditions of the triangle inequality theorem are satisfied, we can conclude that a triangle can be formed with side lengths 6, 9, and 12.

Therefore, the correct answer is:
Yes, because [tex]\(6 + 9 > 12\)[/tex].
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