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Could
10.6cm,5.6cm, and
4.0cm be the side lengths of a triangle?
Choose 1 answer:
(A) Yes
(B) No

Could $10.6 \mathrm{~cm}, 5.6 \mathrm{~cm}$ , and $4.0 \mathrm{~cm}$ be the side lengths of a triangle? $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No

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

Full solution

Q. Could

10.6 \mathrm{~cm}, 5.6 \mathrm{~cm}

, and

4.0 \mathrm{~cm}

be the side lengths of a triangle?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(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.
Calculate Sum of Two Shorter Sides: First, we check if the sum of the two shorter sides, $5.6\,\text{cm}$ and $4.0\,\text{cm}$ , is greater than the longest side, $10.6\,\text{cm}$ . We calculate $5.6 + 4.0$ and compare it to $10.6$ .
Verify Theorem Not Satisfied: The sum of the two shorter sides is $5.6 + 4.0 = 9.6\,\text{cm}$ , which is not greater than the longest side, $10.6\,\text{cm}$ . This means that the Triangle Inequality Theorem is not satisfied.
Conclusion: Since the sum of the lengths of the two shorter sides is not greater than the length of the longest side, the lengths $10.6\,\text{cm}$ , $5.6\,\text{cm}$ , and $4.0\,\text{cm}$ cannot form a triangle.

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