In the given figure- AD is median of - ABC and E is any point on median AD- If Area - ABE - xArea - ACE-Then find x

Since AD is the median of #160; #916;ABC , therefore it will divide #160; #916;ABC into triangles of equal areas that is #160; Ar( #916;A ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

The Centroid

In the given ...

Question

In the given figure; AD is median of $Δ A B C$ and E is any point on median AD. If Area ( $Δ A B E$ ) = $x$ Area ( $Δ A C E$ ).Then find $x$

Open in App

Solution

Since AD is the median of $Δ A B C$ , therefore it will divide $Δ A B C$ into triangles of equal areas that is $A r (Δ A B D) = A r (Δ A C D)$ .........( eqn 1)

Also ED is the median of $Δ E B C$ , therefore, $A r (Δ E B D) = A r (Δ E C D)$ ..........( eqn 2)

On subtracting equation 2 from 1, we get

$A r (Δ A B D) - A r (Δ E B D) = A r (Δ A C D) - A r (Δ E C D)$

$A r (Δ A B E) = A r (Δ A C E)$

$∴ x = 1$

Suggest Corrections

Similar questions

Q. If E is the mid point of median AD in triangle ABC, then prove that :
Area (

Δ A B E

) =

\frac{1}{4}

Area (

Δ A B C

State true or false:

In the given figure;

A D

is median of

△ A B C

and

E

is any point on median

A D

. Prove that Area

(△ A B E)

= Area

(△ A C E)

In the given figure AD is median of $Δ A B C$ , DE is median of $Δ A B D$ and EF is median of $Δ B E D$ . If area of $Δ A B C$ is $128 c m^{2}$ , then area of $Δ B E F$ is

Q. In the given

Δ A B C

, Z is the mid-point of the median AD. If the area of

Δ A B C

18 m^{2}

, find the area of

Δ B Z C

Q. In given figure,

E

is any point on median

A D

of a

△ A B C

. Show that

a r e a (A B E) = a r e a (A C E)

Join BYJU'S Learning Program

In the given figure; AD is median of ΔABC and E is any point on median AD. If Area (ΔABE) = xArea (ΔACE).Then find x

In the given figure; AD is median of $Δ A B C$ and E is any point on median AD. If Area ( $Δ A B E$ ) = $x$ Area ( $Δ A C E$ ).Then find $x$