Could 10.6\text{ cm}, 5.6\text{ cm},10.6 cm,5.6 cm,10, point, 6, start text, space, c, m, end text, comma, 5, point, 6, start text, space, c, m, end text, comma and 4.0\text{ cm}4.0 cm4, point, 0, start text, space, c, m, end text be the side lengths of a triangle?

A triangle cannot be formed with given side lengths.

Step-by-step explanation:

Given:

First side = 10.6 cm

second side = 5.6 cm

third side = 4.0 cm

We need to find whether these data can be the side lengths of the triangle.

Solution:

Now we know that;

By triangle Inequality property which states that;

"The sum of two side of the triangle must be greater than third side."

All the three condition must be fulfilled.

So checking for all three conditions we get;

1) First side + Second side > Third side

Hence this condition is True.

2) Second side + Third side > First side

Hence this condition is False.

3) Third side + First side > Second side.

Hence this condition is True.

1 out of 3 condition is False and according to triangle property all 3 condition must be True.

Hence a triangle cannot be formed with given side lengths.