Question

Can 6,12, and 18 make a triangle?

Answer 1

By definition, 3 side lengths are a triangle if any 2 side lengths add up to be greater than the third.

We can already see that the side lengths 6 and 12 will add up to a value of 18, which is equal to the last side length, meaning that the three values are not a triangle.

`a=6`

`b=12`

`c=18`

`a+b>c`

`b+c>a`

`c+a>b`

`6+12>18` (Since this is not true, this is not a triangle)

Hope this helps.

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Answer 2

The combination of side lengths 6, 12, and 18 violates the Triangle Inequality Theorem, which states that the sum of any two sides must be greater than the third. Therefore, these three lengths cannot form a triangle.

No, 6, 12, and 18 cannot form a triangle.

The Triangle Inequality Theorem states that for any three side lengths of a triangle, the sum of any two of the side lengths must be greater than the third side length. In this case, 6 + 12 = 18, which is equal to the third side length. Therefore, it is not possible to form a triangle with these side lengths.

For example, if we try to form a triangle with these side lengths, we can arrange the sides in a line: 6, 12, 18. However, this does not form a closed figure, which is a necessary condition for a triangle.

Therefore, we can conclude that 6, 12, and 18 cannot form a triangle.