Question

The bisector of $\angle A$ and $△ABC$ intersects $\overline{BC}$ in $D$. If $AB:AC=2:3$ and $BC=12.5$ then $BD=$

• A. $6.25$
• B. $7.50$
• C. $6.0$
• D. $5.0$

Answer 1

The correct option is A $6.25$

$AB:AC=2:3$ & $BC=12.5,BD=?$Let $BD=x$Here, $\frac{AB}{AC}=\frac{BD}{CD}$$\frac{2}{3}=\frac{x}{12.5-x}$$2(12.5-x)=3x$$25-2x=3x$$5x=25=x=5cm=BD$

$\therefore BD=5cm$