Question

A triangle has side lengths of 3 inches, 7 inches, and c inches.

Enter values to write an inequality that describes the possible values for c, the length of the third side of the triangle

? < c < ?

Answer 1

4 < c < 10

Explanation:

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Answer 2

The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

You can say that
`7+3\ \textgreater \ c`,
`c+7\ \textgreater \ 3`, and
`c+3\ \textgreater \ 7`. Simplifying,
`c\ \textless \ 10` and
`c\ \textgreater \ 4`, so
`4\ \textless \ c\ \textless \ 10`.