the sum of the lengths of any two sides of a triangle must be greater that the length of the third side. what are the possible valuse of x for this triangle. if the sides are (x+5)cm, and (3x)cm, and 40cm

To find the possible values of x for this triangle, we need to apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's apply the theorem to the given sides:
(x + 5) cm + (3x) cm > 40 cm
Combine like terms:
4x + 5 cm > 40 cm
Subtract 5 cm from both sides:
4x > 35 cm
Divide both sides by 4:
x > 8.75 cm

Therefore, the possible values of x for this triangle are x > 8.75 cm. This means that x must be greater than 8.75 cm for the triangle to be valid.