Final answer:
To find the value of x and the measure of AB in triangle ABC, we use the triangle inequality theorem and solve an equation to determine the value of x. The measure of AB is then calculated by substituting the value of x into the given equation.
Step-by-step explanation:
To find the value of x and the measure of AB, we can use the fact that the sum of the lengths of two sides of a triangle is always greater than the length of the third side.
Applying this to triangle ABC, we have AB + BC > AC.
Substituting the given values, we get 5x + 13 + 65 > 123. Simplifying this inequality, we have 5x + 78 > 123. Subtracting 78 from both sides, we get 5x > 45. Dividing both sides by 5, we find that x > 9. Therefore, the value of x is greater than 9.
Now let's find the measure of AB. Substituting x = 9 into the equation AB = 5x + 13, we get AB = 5(9) + 13 = 45 + 13 = 58. Therefore, the measure of AB is 58 units.
Learn more about Triangle Inequality Theorem