Questions: Can the sides of a triangle have lengths 2.6, 7.8, and 9.7?

Transcript text: Can the sides of a triangle have lengths $2.6,7.8$, and $9.7 ?$ yes no Submit

Solution

Solution Steps

Step 1: Identify the Triangle Inequality Theorem

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Step 2: Check the First Condition

Check if the sum of the lengths of the first two sides is greater than the length of the third side:
$ 2.6 + 7.8 > 9.7 $

Step 3: Check the Second Condition

Check if the sum of the lengths of the first and third sides is greater than the length of the second side:
$ 2.6 + 9.7 > 7.8 $

Step 4: Check the Third Condition

Check if the sum of the lengths of the second and third sides is greater than the length of the first side:
$ 7.8 + 9.7 > 2.6 $

Final Answer

The correct answer is no.

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