Question

Can 3,6,9 form a triangle ?

Answer 1

The lines will form a straight line not a triangle.

Explanation:

Sides of length `3, 6 and 9` will form a straight line, not a triangle.

The reason for this is that `3+6=9`, If the three lines are drawn, the two shorter lines (`3+6`) will be the same as the longer line (`9`). There will be no 'height'.

For three lengths to form a triangle, the sum of two of the sides has to be more than the length of the third line.

`3,6,8 " or " 3,6,7` will form triangles.

Answer 2

`color(red)("Not Possible"`

Explanation:

`color(indigo)("The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side."`

Since 3 + 6 = 9, the third side, we cannot form a triangle with sides measuring 3, 6, 9.