You visited us 1 times! Enjoying our articles? Unlock Full Access!

Pythagoras Theorem

Let ABC be ...

Question

Let $A B C$ be a triangle with $∠ B = 90^{\circ}$ . Let $A D$ be the bisector of $∠ A$ with $D$ on $B C$ . Suppose $A C = 6 c m$ and the area of the triangle $A D C$ is $10 c m^{2}$ , Then the length of $B D$ in $c m$ is equal to

\frac{3}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3}{10}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{5}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{10}{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{10}{3}$
Angle bisector theorem
$\frac{x}{6} = \frac{y}{z}$
$\Rightarrow x z = 6 y$
$\Rightarrow 20 = 6 y$
$\Rightarrow y = \frac{10}{3} c m$

Suggest Corrections

Similar questions

Q. Let

A B C

be a right triangle with length of side

A B = 3

and hypotenuse

A C = 5

. If

D

is a point on

B C

such that

\frac{B D}{D C} = \frac{A B}{A C}

, then

A D

is equal to:

Q. Let

A B C

be a triangle with

∠ A = 45^{\circ}

. Let

P

be a point on the side

B C

with

P B = 3

and

P C = 5

. If

^{'} O^{'}

is the circumcentre of the triangle

A B C

then the length

O P

is equal to

Q. Let

A B C

be an isosceles triangle with

A B = A C

. Suppose that the angle bisector of angle

B

meets the side

A C

at a point

D

such that

B C = B D + A D

. Measure of the angle

A

in degrees, is

Q. Let ABC be a triangle with

∠

A =

45^{0}

. Let P be a point on the side BC with PB = 3 and PC = 5. If 'O' is the circumcenter of the triangle ABC then the length of OP is equal to -

Let ABC be a triangle with

∠ A = 45^{\circ}

. Let P be a point on side BC with

P B = 3

and

P C = 5

O

is circumcenter of triangle ABC, then length

O P

is?

Join BYJU'S Learning Program

Let ABC be a triangle with ∠B=90∘ . Let AD be the bisector of ∠A with D on BC . Suppose AC=6cm and the area of the triangle ADC is 10cm2, Then the length of BD in cm is equal to

The correct option is D 103Angle bisector theoremx6=yz⇒xz=6y⇒20=6y⇒y=103cm

Let $A B C$ be a triangle with $∠ B = 90^{\circ}$ . Let $A D$ be the bisector of $∠ A$ with $D$ on $B C$ . Suppose $A C = 6 c m$ and the area of the triangle $A D C$ is $10 c m^{2}$ , Then the length of $B D$ in $c m$ is equal to

The correct option is D $\frac{10}{3}$
Angle bisector theorem
$\frac{x}{6} = \frac{y}{z}$
$\Rightarrow x z = 6 y$
$\Rightarrow 20 = 6 y$
$\Rightarrow y = \frac{10}{3} c m$