Could 10.5\text{ cm}, 8.0\text{ cm},10.5 cm,8.0 cm,10, point, 5, start text, space, c, m, end text, comma, 8, point, 0, 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?

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:

      True

    True

 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.

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