Answer:
AB = 54
Step-by-step explanation:
AB = AC
4x+6 = 5x-6
Subtract 4x from each side
4x+6-4x = 5x-6-4x
6 = x-6
Add 6 to each side
6+6 =x
12 =x
We want to find AB
AB =4x+6
4(12)+6
48+6
54
AB=54
in Δs ABD and ACD
BD=CD (given)
∠ADB=∠ADC (each right angle)
AD=AD (common)
∴ ΔABD≅ΔACD
so AB=AC
4x+6=5x-6
6+6=5x-4x
x=12
AB=4×12+6=48+6=54
