Final answer:
By setting AD equal to DB since CD is a median, we solve the equation 3x + 10 = 7x + 2 to find x. Then, we calculate the length of AB as the sum of AD and DB to find that AB = 32 units.
Step-by-step explanation:
In the given triangle △ABC, we have the information that CD is a median and we are given the lengths of AD and DB in terms of x which are AD = 3x + 10, and DB = 7x + 2. Since CD is a median, it divides side AB into two segments of equal length, meaning AD = DB. Therefore, we can set up the equation 3x + 10 = 7x + 2 to find the value of x.
Solving the equation:
3x + 10 = 7x + 2
10 - 2 = 7x - 3x
8 = 4x
x = 2
With x found, we can determine the length of AB by adding the lengths of AD and DB:
AB = AD + DB
AB = (3x + 10) + (7x + 2)
AB = (3(2) + 10) + (7(2) + 2)
AB = (6 + 10) + (14 + 2)
AB = 16 + 16
AB = 32
So the length of AB is 32 units.