Question

The ratio of the lengths of the three line segments is 1 : 2 : 3. If the sum of their lengths is 12 cm, can these line segments form a triangle?

Answer 1

Answer:

No, these lines cannot form a triangle

Explanation:

If the ratio is 1:2:3,

then for eg the lengths of sides are 2,4,6 cm respectively.

But According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side.

So here,

2+4 = 6 = 6

2+6 = 12 > 4

4+6 = 10 > 2

So, no these line segments cannot form a triangle.

I hope this helps:)