Question

In the figure, the length of $\overline{AC}$ is $3$ times the length of $\overline{CD}$. If B is the midpoint of $\overline{AC}$, and the length of $\overline{CD}$ is $5$, calculate the length of $\overline{BD}$.

• A. $10$
• B. $12.5$
• C. $13.5$
• D. $15$

Answer 1

The correct option is B $12.5$

Given, $AC=3CD$ and $CD=5$

$\Rightarrow AC=3\times 5=15$

Also given, $B$ is mid point of $AC$

$\Rightarrow BC=\frac{AC}{2}=\frac{15}{2}=7.5$

$\Rightarrow BD=BC+CD=7.5+5=12.5$