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Could
10.7cm,3.2cm, and
5.5cm be the side lengths of a triangle?
Choose 1 answer:
(A) Yes
(B) No

Could $10.7 \mathrm{~cm}, 3.2 \mathrm{~cm}$ , and $5.5 \mathrm{~cm}$ 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

10.7 \mathrm{~cm}, 3.2 \mathrm{~cm}

, and

5.5 \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.
Check $10.7\,\text{cm} + 3.2\,\text{cm} > 5.5\,\text{cm}$ : First, we check if $10.7\,\text{cm} + 3.2\,\text{cm} > 5.5\,\text{cm}$ . Performing the calculation, we get $13.9\,\text{cm} > 5.5\,\text{cm}$ , which is true.
Check $10.7\,\text{cm} + 5.5\,\text{cm} > 3.2\,\text{cm}$ : Next, we check if $10.7\,\text{cm} + 5.5\,\text{cm} > 3.2\,\text{cm}$ . Performing the calculation, we get $16.2\,\text{cm} > 3.2\,\text{cm}$ , which is true.
Check $3.2\,\text{cm} + 5.5\,\text{cm} > 10.7\,\text{cm}$ : Finally, we check if $3.2\,\text{cm} + 5.5\,\text{cm} > 10.7\,\text{cm}$ . Performing the calculation, we get $8.7\,\text{cm} > 10.7\,\text{cm}$ . This is not true, which means the Triangle Inequality Theorem is not satisfied for these side lengths.
Conclusion: Since one of the conditions of the Triangle Inequality Theorem is not met, the lengths $10.7\,\text{cm}$ , $3.2\,\text{cm}$ , and $5.5\,\text{cm}$ cannot form the sides of a triangle.

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