Question

Which best describes the construction of a triangle if given the segment lengths of 10 cm, 5 cm, and 4 cm?

Answer 1

It can't be constructed.
The lengths of 4 cm and 5 cm add to 9 cm and that is one too centimeter too short to make an angle with the 3rd side.

Answer 2

It is not possible to construct a triangle with the given side lengths.

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:

`5+10>4`

`15>4`

Now check another side.

`5+4>10`

`9\\gtr 10`

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.