Yes they could. The only requirement is that if you add any two sides together they are longer than the third. 19 + 13 > 14; 19 + 14 > 13, and 13 + 14 > 19, so those sides can make a triangle.
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An scalene triangle.
To check whether it is possible to have a triangle with side lengths 4cm, 13cm, and 14cm, we use a special rule.The rule is: If you take any two sides of a triangle and add their lengths, the sum of the lengths must be greater than the third side.Test this triangle. 4+13=17, which is bigger than 14. 14+4=18, which is bigger than 13. 13+14=27, which is greater than 4.The rule works for all side combinations, so it is possible to have a triangle like this.So the answer is: yes, you can have a triangle of side lengths 4cm, 13cm, 14cm. (Note that the lengths do not have to be in centimeters, for example they can be 4m, 13m, and 14m)
it is an acute triangle.
By Pythagoras's theorem, to make a right angled triangle, 142 + 152 should be 212 But 142 + 152 = 196 + 225 = 421 whereas 212 = 441 So these three sides cannot make a right angled triangle.
For a triangle to exist, the sum of the two shorter sides must be longer than the longest side. If 15 is the longest side, then the other, missing, shorter side must be greater than 15 - 4 = 11. If the third, missing, side is the longest side, then it must be less than 15 + 4 = 19 So the third side is any length greater than 11 and less than 19. Examples include 12, 13, 15, 11.5, 18.5.