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The lengths of two sides of a triangle are 6 and 13. Which can be the length of the third side?

Answer 1

Jayden Jackson

Length of the third side will have a value between #7 and 19#.

The sum of the lengths of any two sides of a triangle must be greater than the third side.

#=># the third side must be greater than #13-6=7#, and the third side must be less than #6+13=19#

Denoting the third side as #x#, #=> 7 < x< 19#

Hence, #x# will have a value between #7 and 19#

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Answer 2

Ella Armstrong

To determine the possible lengths of the third side of the triangle, you can 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.

So, for a triangle with sides of lengths 6 and 13:

The third side must be greater than the difference between the lengths of the other two sides.
The third side must be less than the sum of the lengths of the other two sides.

Therefore, the possible lengths of the third side can be:

6 + 13 > Third side > |6 - 13|

Solve for both inequalities:

6 + 13 > Third side 19 > Third side

|6 - 13| = |-7| = 7 7 < Third side

So, the third side must be greater than 7 and less than 19. Therefore, the possible lengths of the third side are any value between 7 and 19, exclusive.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.