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 < >>
What inequality represents possible values for the length of the third side of a triangle with side lengths of 3 inches, 7 inches, and c inches?
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To find the possible values for ( c ), we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given the side lengths 3 inches, 7 inches, and ( c ) inches, we can set up the following inequalities:
1. ( 3 + 7 > c ) → ( c < 10 ) 2. ( 3 + c > 7 ) → ( c > 4 )
3. ( 7 + c > 3 ) → ( c > -4 ) (This inequality is always true since ( c ) must be positive.)
So the relevant inequalities for ( c ) are ( c < 10 ) and ( c > 4 ).
Putting this together, the possible values for ( c ) can be described by the inequality:
[ 4 < c < 10 ]
This means ( c ) must be more than 4 inches and less than 10 inches. If you have any more questions or need further clarification, feel free to ask!