Answer:
AB = 24.
Step-by-step explanation:
BD = 5x – 26.
BC = 2x + 1.
AC = 43.
Applying the segment addition postulate, AC = AB + BC.
Since BD is equal to BC, with BD being expressed as 5x-26 and BC as 2x+1, we can create an equation to calculate x:
5x - 26 = 2x + 1 Subtract 2x from both sides.
5x - 26 - 2x = 2x + 1 - 2x.
3x-26 = 1 Add 26 to both sides.
3x-26 + 26 = 1 + 26.
3x = 27 Divide each side by 3.
3x/3 = 27/3.
x = 9.
Thus, BC = 2x + 1 = 2(9) + 1 = 18 + 1 = 19.
Since AC = AB + BC; using the data provided along with the found BC value, we get:
43 = AB + 19 Subtract 19 from each side.
43 - 19 = AB + 19 - 19.
24 = AB.
