Answer:
Yes, 10.5 cm, 8.0 cm and 4.0 cm can be the side lengths of a triangle.
Step-by-step explanation:
We have been given three lengths as 10.5 cm, 8.0 cm and 4.0 cm. We are asked to determine whether these side can be the side lengths of a triangle.
We will use triangle inequality theorem to solve our given problem.
Triangle inequality theorem states that sum of two sides of a triangle must be greater than 3rd side. Using triangle inequality theorem we will get 3 inequalities as:
[tex]10.5+8.0>4.0[/tex]
[tex]18.5>4.0[/tex] True
[tex]8.0+4.0>10.5[/tex]
[tex]12.0>10.5[/tex] True
[tex]10.5+4.0>8.0[/tex]
[tex]14.5>8.0[/tex] True
Since all the three side lengths satisfy triangle inequality theorem, therefore, 10.5 cm, 8.0 cm and 4.0 cm can be the side lengths of a triangle.
