Question

The length of the line segments $\text{AB}$ and $\text{BD}$ are in the ratio $2:3$. If the length of the line segment $\text{AD}$ is $30$ units, what are the lengths of $\text{AB}$ and $\text{BD}?$

• A. $12,18$
• B. $14,16$
• C. $16,14$
• D. $18,12$

Answer 1

The correct option is A $12,18$

Given ratio: $2:3$


Length of $\text{AD}=30$ units

Now,
Let the length of the line segment $\text{AB}$ be $2x$ unit and the length of the line segment $\text{BD}$ be $3x$ units.

$\because \text{AD}=\text{AB}+\text{BD}$

$\therefore 30=2x+3x$

$5x=30$

$x=6$

$\Rightarrow$ Length of the line segment $\text{AB}=12$ units

$\Rightarrow$ Length of the line segment $\text{BD}=18$ units