Answer:
Yes
Step-by-step explanation:
You must be able to add any two sides and get a number greater than the third side, in this case, that is possible.
A triangle with side lengths as of 15 units, 12 units and 9 units exist.
Suppose that we want to check if
a, b and c units.
can be sides of a triangle or not.
Then, if these three values satisfy the relation:
[tex]a < b +c\\b < a + c\\c < a + b[/tex]
Then they are for sure side length of a triangle.
(these 3 relation just checks if sum of any two sides is bigger than the third side) (refer triangle inequality theorem to know more on it).
Triangle inequality theorem of a triangle says that the sum of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]
For this case, we have a = 15, b = 12, and c = 9
Thus, as we have:
15 < 12 + 9
9 < 12 + 15
12 < 15 + 9
Thus, a triangle with side lengths as of 15 units, 12 units and 9 units exist.
Learn more about the triangle inequality theorem here;
https://brainly.com/question/342881
