Could 12.2cm,6.0cm, and 4.2cm be the side lengths of a triangle? Choose 1 answer: (A) Yes (B) No

Check Triangle Inequality Theorem: To determine if three lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. We will check this for all three combinations of sides. Check 1st Combination: First, we check if 12.2cm + 6.0cm > 4.2cm. Performing the calculation, we get 18.2cm > 4.2cm, which is true. Check 2nd Combination: Next, we check if 12.2cm + 4.2cm > 6.0cm. Performing the calculation, we get 16.4cm > 6.0cm, which is also true. Check 3rd Combination: Lastly, we check if 6.0cm + 4.2cm > 12.2cm. Performing the calculation, we get 10.2cm > 12.2cm, which is not true. Final Conclusion: Since the sum of the lengths of the two smaller sides (6.0cm and 4.2cm) is not greater than the length of the longest side (12.2cm), the lengths 12.2cm, 6.0cm, and 4.2cm cannot form a triangle according to the triangle inequality theorem.

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Could
12.2cm,6.0cm, and
4.2cm be the side lengths of a triangle?
Choose 1 answer:
(A) Yes
(B) No

Could $12.2 \mathrm{~cm}, 6.0 \mathrm{~cm}$ , and $4.2 \mathrm{~cm}$ be the side lengths of a triangle? $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) $\mathrm{No}$

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Algebra 2

Is (x, y) a solution to the system of equations?

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Q. Could

12.2 \mathrm{~cm}, 6.0 \mathrm{~cm}

, and

4.2 \mathrm{~cm}

be the side lengths of a triangle?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B)

\mathrm{No}

Check Triangle Inequality Theorem: To determine if three lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. We will check this for all three combinations of sides.
Check $1$ st Combination: First, we check if 12.2\,\text{cm} + 6.0\,\text{cm} > 4.2\,\text{cm}. Performing the calculation, we get 18.2\,\text{cm} > 4.2\,\text{cm}, which is true.
Check $2$ nd Combination: Next, we check if 12.2\,\text{cm} + 4.2\,\text{cm} > 6.0\,\text{cm}. Performing the calculation, we get 16.4\,\text{cm} > 6.0\,\text{cm}, which is also true.
Check $3$ rd Combination: Lastly, we check if 6.0\,\text{cm} + 4.2\,\text{cm} > 12.2\,\text{cm}. Performing the calculation, we get 10.2\,\text{cm} > 12.2\,\text{cm}, which is not true.
Final Conclusion: Since the sum of the lengths of the two smaller sides ( $6.0\,\text{cm}$ and $4.2\,\text{cm}$ ) is not greater than the length of the longest side ( $12.2\,\text{cm}$ ), the lengths $12.2\,\text{cm}$ , $6.0\,\text{cm}$ , and $4.2\,\text{cm}$ cannot form a triangle according to the triangle inequality theorem.