Answer:
C. 54
Explanation:
The triangles ABD and ACD are congruent by SAS (Side - angle - side) becuase
AD is congruent to itself
∠ADB = ∠ADC
BD is congruent to CD
So, the length of AB is equal to the length of AC and we can write the following equation
AB = AC
4x + 6 = 5x - 6
Solving for x, we get:
4x + 6 + 6 = 5x - 6 + 6
4x + 12 = 5x
4x + 12 - 4x = 5x - 4x
12 = x
Then, the length of AB is
AB = 4x + 6
AB = 4(12) + 6
AB = 48 + 6
AB = 54
Therefore, the answer is
C. 54
