Could 13.5cm,8.0cm, and 3.5cm be the side lengths of a triangle? Choose 1 answer: (A) Yes (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 8.0cm and 3.5cm, and the longest side is 13.5cm. We calculate 8.0cm + 3.5cm and compare it to 13.5cm. Calculate Sum: The sum of the two shortest sides is 8.0cm + 3.5cm = 11.5cm. This sum must be greater than the longest side, which is 13.5cm, to satisfy the Triangle Inequality Theorem. Verify Triangle Formation: Since 11.5cm is not greater than 13.5cm, the lengths 13.5cm, 8.0cm, and 3.5cm do not satisfy the Triangle Inequality Theorem and therefore cannot form a triangle.

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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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Algebra 2

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.