Math Is Fun Forum

handlerone

Guest

Geometry

7. Each set of numbers below represents the lengths of three line segments.
Which set represent line segments that could be connected to form a triangle:

A. (1, 2, 3)
B. (3, 4, 5)
C. (1, 10, 100)
D. (1, 2, 5)
E. (1, 3, 4)
F. (1, 20, 100)

I don't understand how to do this

Phrzby Phil

Member

From: Richmond, VA

Registered: 2022-03-29

Posts: 17

Re: Geometry

Think of it this way..

The shortest distance between 2 points is a straight line.

If the sum of the lengths of 2 side of a triangle = the length of the third, then the "triangle" would collapse to 2 overlapping straight lines.

If the sum of the lengths of 2 side of a triangle is < the length of the third, then the shortest distance between the third line's endpoints would not be that straight line.

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World Peace Thru Frisbee

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,257

Re: Geometry

Hi handlerone,

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not possible for that sum to be less than the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality.

Hence, the solution is B.

Please see the link.

Triangle Inequality Theorem.

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