Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. in the figure, $overline{cd}$ is the perpendicular bisector of $overline{ab}$. if the length of $overline{ac}$ is $2x$ and the length of $overline{bc}$ is $3x - 5$, the value of $x$ is .

Explanation:

Step1: Apply perpendicular - bisector property

Since $CD$ is the perpendicular bisector of $AB$, by the perpendicular - bisector theorem, $AC = BC$.
So, we set up the equation $2x=3x - 5$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides of the equation: $0 = 3x-2x - 5$.
Simplify to get $0=x - 5$.
Add 5 to both sides: $x = 5$.

Answer:

5