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Could
13.5cm,8.0cm, and
3.5cm be the side lengths of a triangle?
Choose 1 answer:
(A) Yes
(B) No

Could $13.5 \mathrm{~cm}, 8.0 \mathrm{~cm}$ , and $3.5 \mathrm{~cm}$ 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

13.5 \mathrm{~cm}, 8.0 \mathrm{~cm}

, and

3.5 \mathrm{~cm}

be the side lengths of a triangle?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B) No

Use Triangle Inequality Theorem: To determine if three lengths can form a triangle, we can 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.
Check Shortest Sides: First, we check if the sum of the two shortest sides is greater than the longest side. The two shortest sides are $8.0\,\text{cm}$ and $3.5\,\text{cm}$ , and the longest side is $13.5\,\text{cm}$ . We calculate $8.0\,\text{cm} + 3.5\,\text{cm}$ and compare it to $13.5\,\text{cm}$ .
Calculate Sum: The sum of the two shortest sides is $8.0\,\text{cm} + 3.5\,\text{cm} = 11.5\,\text{cm}$ . This sum must be greater than the longest side, which is $13.5\,\text{cm}$ , to satisfy the Triangle Inequality Theorem.
Verify Triangle Formation: Since $11.5\,\text{cm}$ is not greater than $13.5\,\text{cm}$ , the lengths $13.5\,\text{cm}$ , $8.0\,\text{cm}$ , and $3.5\,\text{cm}$ do not satisfy the Triangle Inequality Theorem and therefore cannot form a triangle.

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