Question

The ratio of the lengths of the three line segments is 1 : 2 : 3. If the sum of their lengths is 18 cm. Find the length of the three line segments. Can there three line segments form a triangle ? (Justify your answer)​

Answer 1

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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:)

Answer 2

Answer:

This is the answer for your question.

Step-by-step explanation:

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 three line segments form a triangle?

Answer

Let the segments be x,2x,3x

x+2x+3x=12

6x=12

x=2

2,4,6

According to triangle in equality

sum of there sides > third sides

2+4=6>6 false

∴ triangle cannot be formed.