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Could
7.7cm,4.0cm, and
1.7cm be the side lengths of a triangle?
Choose 1 answer:
(A) Yes
(B) No

Could $7.7 \mathrm{~cm}, 4.0 \mathrm{~cm}$ , and $1.7 \mathrm{~cm}$ 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

7.7 \mathrm{~cm}, 4.0 \mathrm{~cm}

, and

1.7 \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 Shorter Sides: First, we check if the sum of the two shorter sides, $4.0\,\text{cm}$ and $1.7\,\text{cm}$ , is greater than the longest side, $7.7\,\text{cm}$ . We calculate $4.0 + 1.7$ and compare it to $7.7$ .
Compare Sum to Longest Side: The sum of the two shorter sides is $4.0\,\text{cm} + 1.7\,\text{cm} = 5.7\,\text{cm}$ , which is not greater than the longest side, $7.7\,\text{cm}$ . 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 $7.7\,\text{cm}$ , $4.0\,\text{cm}$ , and $1.7\,\text{cm}$ cannot form a triangle.

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