Answer:
It is not possible to construct a triangle with the given side lengths.
Step-by-step explanation:
We have been given three segment lengths and we are asked to describe about the construction of a triangle with given lengths: 10 cm, 5 cm, and 4 cm.
We will use triangle inequality theorem to answer our given problem.
Triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
So let us check our given using triangle inequality theorem as:
[tex]5+10>4[/tex]
[tex]15>4[/tex]
Now check another side.
[tex]5+4>10[/tex]
[tex]9\ngtr 10[/tex]
Since the sum of our given two sides is less than third side, therefore, we can not construct a triangle with our given side lengths.
