It's possible to build a triangle with side lengths of 5 5 and 10?

Answer 1

No, geometrically we call that a line.

The sum of the two shortest sides must be greater than the longest side to make a triangle.

So it is possible to have a triangle with the sides of 10, 5, and 5.0000000001

So long as the sum of the two shortest sides is greater (it does not matter how much greater) it is a triangle.

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Another contributor came at the question from a different direction, and had a different answer:

Technically, yes. But you wouldn't recognize it as a triangle.

It would look like a line segment with a length of 10.

Lengths of sides: 5, 5, and 10

Angles: 0°, 180°, 0°

Length of base: 10

Height: zero

Area: zero