The diagonals of rectangle ABCD intersect at point Z. DZ = x + 6 and AC = 5x + 3 find the length of AC

AC=BD, therefore
AC=BZ+ZD
[tex]\begin{gathered} 5x+3=x+6+x+6 \\ 5x+3=2x+12 \\ 5x+3-2x=2x+12-2x \\ 3x+3=12 \\ 3x+3-3=12-3 \\ 3x=9 \\ \frac{3x}{3}=\frac{9}{3} \\ x=3 \end{gathered}[/tex]then
[tex]AC=5x+3=5(3)+3=15+3=18[/tex]answer: AC= 18