Answer:
AC = 50
Step-by-step explanation:
Since, B is the midpoint of AC.
[tex]\therefore AB = BC\\
\therefore x^2 = 4x + 5\\
\therefore x^2 - 4x - 5 =0\\
\therefore x^2 - 5x + x - 5= 0\\
\therefore x(x - 5) +1(x - 5)=0\\
\therefore (x - 5)(x + 1) =0\\
\therefore x - 5 = 0\: or \: x + 1 = 0\\
\therefore x = 5 \: or \: x = - 1\\ \because x = - 1 \: doesn't \: satisfy\: the\: \\condition \: of \: midpoint \\
\therefore x =5\\
\because AC = AB + BC\\
\therefore AC = x^2 + 4x + 5\\
\therefore AC = x^2 + 4x + 5 \\
\therefore AC = 5^2 + 4\times 5 + 5\\
\therefore AC = 25 + 20 +5\\
\huge \red {\boxed {\therefore AC = 50}} [/tex]
