(D) In $\triangle ABC$,$\angle B = 90^{\circ}$. $AD$ is the angle bisector of $\angle A$. Draw a perpendicular from $D$ to $AC$,let it be $DE$. Since

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) In $\triangle ABC$,$\angle B = 90^{\circ}$. $AD$ is the angle bisector of $\angle A$. Draw a perpendicular from $D$ to $AC$,let it be $DE$. Since $AD$ is the angle bisector,$DE = DB$ (distance from bisector to sides). Area of $\triangle ADC = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times AC \times DE = 10$. Given $AC = 6 \text{ cm}$,we have $\frac{1}{2} \times 6 \times DE = 10$. $3 \times DE = 10 \implies DE = \frac{10}{3} \text{ cm}$. Since $DB = DE$,the length of $BD$ is $\frac{10}{3} \text{ cm}$.

Class 11 Mathematics Straight Lines Problems related to triangle and quadrilateral

Difficult

Let $ABC$ be a triangle with $\angle B = 90^{\circ}$. Let $AD$ be the bisector of $\angle A$ with $D$ on $BC$. Suppose $AC = 6 \text{ cm}$ and the area of the $\triangle ADC$ is $10 \text{ cm}^2$. Then,the length of $BD$ in $\text{cm}$ is equal to

KVPY 2011 All KVPY

A
$\frac{3}{5}$
B
$\frac{3}{10}$
C
$\frac{5}{3}$
D
$\frac{10}{3}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Lines

Subtopic

Problems related to triangle and quadrilateral

Previous Year

KVPY 2011 Paper All KVPY years →

The base $BC$ of a triangle $ABC$ is bisected at the point $(p, q)$ and the equations of the sides $AB$ and $AC$ are $px + qy = 1$ and $qx + py = 1$. The equation of the median through $A$ is:

View Solution

In a $\triangle ABC$ with $\angle A < \angle B < \angle C$,points $D, E, F$ are on the interior of segments $BC, CA, AB$ respectively. Which of the following triangles cannot be similar to $\triangle ABC$?

DifficultKVPY 2013

View Solution

If $A(4,7)$,$B(-7,8)$,and $C(1,2)$ are the vertices of $\triangle ABC$,then the equation of the perpendicular bisector of the side $AB$ is

MediumAP EAMCET 2021

View Solution

If the points $(1, 1)$,$(-1, -1)$ and $(-\sqrt{3}, k)$ are vertices of an equilateral triangle,then the value of $k$ will be:

Easy

View Solution

If $P(\sin \alpha, \cos \alpha)$ lies inside the triangle formed by the vertices $(0,0), \left(\frac{\sqrt{3}}{2}, 0\right)$ and $\left(0, \frac{\sqrt{3}}{2}\right)$,then $\alpha$ lies in the interval

EasyAP EAMCET 2022

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Let $ABC$ be a triangle with $\angle B = 90^{\circ}$. Let $AD$ be the bisector of $\angle A$ with $D$ on $BC$. Suppose $AC = 6 \text{ cm}$ and the area of the $\triangle ADC$ is $10 \text{ cm}^2$. Then,the length of $BD$ in $\text{cm}$ is equal to

Similar Questions

The base $BC$ of a triangle $ABC$ is bisected at the point $(p, q)$ and the equations of the sides $AB$ and $AC$ are $px + qy = 1$ and $qx + py = 1$. The equation of the median through $A$ is:

In a $\triangle ABC$ with $\angle A < \angle B < \angle C$,points $D, E, F$ are on the interior of segments $BC, CA, AB$ respectively. Which of the following triangles cannot be similar to $\triangle ABC$?

If $A(4,7)$,$B(-7,8)$,and $C(1,2)$ are the vertices of $\triangle ABC$,then the equation of the perpendicular bisector of the side $AB$ is

If the points $(1, 1)$,$(-1, -1)$ and $(-\sqrt{3}, k)$ are vertices of an equilateral triangle,then the value of $k$ will be:

If $P(\sin \alpha, \cos \alpha)$ lies inside the triangle formed by the vertices $(0,0), \left(\frac{\sqrt{3}}{2}, 0\right)$ and $\left(0, \frac{\sqrt{3}}{2}\right)$,then $\alpha$ lies in the interval

Vedclass Test Series

Exam Paper Generator

Online Exam Module