AB=2x, BC=x-3, AC=45
2x + x - 3 = 45
3x - 3 = 45
3x = 48
x = 16
x=16
To find the value of x in the given triangle ABC, we can start by using the fact that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
In this case, we have AB = 2x, BC = x - 3, and AC = 45. So we can write the following inequalities:
AB + BC > AC
2x + (x - 3) > 45
Simplifying the inequality:
3x - 3 > 45
Adding 3 to both sides:
3x > 48
Dividing both sides by 3:
x > 16
So we know that x must be greater than 16. However, we need to check if this value satisfies the other inequality as well.
AB + AC > BC
2x + 45 > x-3
Simplifying the inequality:
x + 48 > 0
Subtracting 48 from both sides:
x > -48
Based on the second inequality, we can see that x needs to be greater than -48. Since we already determined that x must be greater than 16, we can conclude that x should be in the range of (-48, ∞).
Therefore, x can take any value greater than -48 in order for the triangle ABC to be valid.