In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$.
If $AB\ =\ 3.5\ cm$, $AC\ =\ 4.2\ cm$, and $DC\ =\ 2.8\ cm$, find $BD$.
"
Given:
In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$.
$AB\ =\ 3.5\ cm$, $AC\ =\ 4.2\ cm$, and $DC\ =\ 2.8\ cm$.
To do:
We have to find the measure of $BD$.
Solution:
$AD$ is the bisector of $∠\ A$, this implies,
$\angle BAD=\angle CAD$
We know that,
The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the corresponding sides containing the angle.
Therefore,
$\frac{AB}{AC} = \frac{BD}{DC}$
$\frac{3.5}{4.2} = \frac{BD}{2.8}$
$BD = \frac{2.8\times3.5}{4.2}$
$BD = \frac{7}{3}\ cm$
$BD=2.33\ cm$
The measure of $BD$ is $2.33\ cm$. 
- Related Articles
- In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$.If $BD\ =\ 2.5\ cm$, $AB\ =\ 5\ cm$, and $AC\ =\ 4.2\ cm$, find $DC$."\n
- In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$. If $AC\ =\ 4.2\ cm$, $DC\ =\ 6\ cm$, and $BC\ =\ 10\ cm$, find $AB$. "\n
- In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$.If $BD\ =\ 2\ cm$, $AB\ =\ 5\ cm$, and $DC\ =\ 3\ cm$, find $AC$."\n
- In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$. If $AB\ =\ 10\ cm$, $AC\ =\ 14\ cm$, and $BC\ =\ 6\ cm$, find $BD$ and $DC$. "\n
- In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$.If $AB\ =\ 10\ cm$, $AC\ =\ 6\ cm$, and $BC\ =\ 12\ cm$, find $BD$ and $DC$."\n
- In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$.If $AB\ =\ 5.6\ cm$, $BC\ =\ 6\ cm$, and $BD\ =\ 3.2\ cm$, find $AC$."\n
- In a $Δ\ ABC$, $AD$ is the bisector of $∠\ A$, meeting side $BC$ at $D$. If $AB\ =\ 5.6\ cm$, $AC\ =\ 6\ cm$, and $DC\ =\ 3\ cm$, find $BC$."\n
- In figure below, $∠\ ABC\ =\ 90^o$ and $BD\ ⊥\ AC$. If $AC\ =\ 5.7\ cm$, $BD\ =\ 3.8\ cm$ and $CD\ =\ 5.4\ cm$, find $BC$."\n
- In figure below, check whether AD is the bisector $\angle A$ of $\triangle ABC$ in each of the following:$AB=5\ cm, AC=10\ cm, BD=1.5\ cm$ and $CD=3.5\ cm$"\n
- In a $Δ\ ABC$, $D$ and $E$ are points on $AB$ and $AC$ respectively, such that $DE\ ∥\ BC$. If $AD\ =\ 2.4\ cm$, $AE\ =\ 3.2\ cm$, $DE\ =\ 2\ cm$ and $BC\ =\ 5\ cm$. Find $BD$ and $CE$. "\n
- In a $Δ\ ABC,$ $D$ and $E$ are points on the sides $AB$ and $AC$ respectively. For each of the following cases show that $DE\ ∥\ BC$: $AB\ =\ 10.8\ cm$, $BD\ =\ 4.5\ cm$, $AC\ =\ 4.8\ cm$, and $AE\ =\ 2.8\ cm$. "\n
- In figure below, $∠\ ABC\ =\ 90^o$ and $BD\ ⊥\ AC$. If $BD\ =\ 8\ cm$, and $AD\ =\ 4\ cm$, find $CD$."\n
- In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$. If $AD\ =\ 2\ cm$, $AB\ =\ 6\ cm$ and $AC\ =\ 9\ cm$, find $AE$. "\n
- In figure below, check whether AD is the bisector $\angle A$ of $\triangle ABC$ in each of the following:$AB=8\ cm, AC=24\ cm, BD=6\ cm$ and $BC=24\ cm$"\n
- In figure below, check whether AD is the bisector $\angle A$ of $\triangle ABC$ in each of the following:$AB=5\ cm, AC=12\ cm, BD=2.5\ cm$ and $BC=9\ cm$"\n
Kickstart Your Career
Get certified by completing the course
Get Started