Answer:
AB = 24
Step-by-step explanation:
BD = 5x – 26
BC = 2x + 1
AC = 43
Using the segment addition postulate, AC = AB + BC.
We know that BD = BC, BD = 5x-26 and BC = 2x+1. We can set up an equation to find the value of x:
5x - 26 = 2x + 1 Subtract 2x from each side
5x - 26 - 2x = 2x + 1 - 2x
3x-26 = 1 Add 26 to each side
3x-26+26 = 1+26
3x=27 Divide both sides by 3
3x/3 = 27/3
x = 9
This means that BC = 2x + 1 = 2(9) + 1 = 18 + 1 = 19.
We know that AC = AB + BC; using our given information as well as the value of BC we just found, we have
43 = AB + 19 Subtract 19 from each side
43 - 19 = AB + 19 - 19
24 = AB
