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Can you construct a triangle that has side lengths 2 in., 3 in., and 6 in.?

Answer 1

See an explanation below:

No, a triangle cannot be constructed with sides of 2 in., 3 in., and 6 in.

For three line segments to be able to form any triangle you must be able to take any two sides, add their length and this sum be greater than the remaining side.

#2"in." + 3"in." = 5"in."#

#5"in." < 6"in."#

For a triangle with sides 3 in., 4 in. and 5 in. which can form a triangle:

3 + 4 = 7 which is greater than 5
3 + 5 = 8 which is greater than 4
4 + 5 = 9 which is greater than 3

The shows the 2 and 3 inch line segments at a #180^o# angle. There is no angle you can put the 2 and 3 inch line segment at which will allow it to be 6 in. long.

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Answer 2

Claire Akin

No, it is not possible to construct a triangle with side lengths 2 in., 3 in., and 6 in.

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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.