Question

AC = CE and D is the midpoint of CE. If CE = 10x + 18, DE = 7x - 1, and BC = 9x-2, find AB.

Answer 1

D is the mid point of CE.

$\begin{gathered} AC\cong CE \\ CE=10x+18 \\ DE=7x-1 \\ BC=9x-2 \\ CD=DE=\frac{1}{2}CE \\ 7x-1=\frac{1}{2}10x+18 \\ 7x-1=\frac{10x+18}{2} \\ 7x-1=5x+9 \\ 7x-5x=9+1 \\ 2x=10 \\ x=\frac{10}{2} \\ x=5 \\ AC=CE=10x+18=10(5)+18=50+18=68 \\ BC=9x-2=9(5)-2=45-2=43 \\ AB=AC-BC=68-43=25 \end{gathered}$