In the right angle triangle $∠ C = 90^{\circ} . A E$ and $B D$ are two medians of a triangle $A B C$ meeting at $F$ . The ratio of the area of $△ A B F$ and the quadrilateral $F D C E$ is

1 : 1

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

1 : 2

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

2 : 1

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

2 : 3

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

Open in App

Solution

The correct option is A $1 : 1$
Triangles BCD, BDA, and ABC has same height and their bases are related by CD = AD = AC/2.
Hence, Area of BCD = Area of BDA = (Area of ABC)/2
Similarly, Area of ABE = Area of ACE = (Area of ABC)/2
So, Area of BCD = Area of ACE
--> (Area of FDCE + Area of BEF) = (Area of FDCE + Area of AFD)
--> Area of BEF = Area of AFD
Now we know, Area of BCD = Area of BDA
--> (Area of FDCE + Area of BEF) = (Area of AFB + Area of AFD)
--> Area of FDCE = Area of AFB
Hence, the required ratio is 1:1.

Suggest Corrections

Similar questions

In the given figure, AE and BD are two medians of $△$ ABC meeting at F. The ratio of the area of $△$ ABF and the quadrilateral FDCE is:

In the given figure, AE and BD are two medians of a $△$ ABC meeting at F. The ratio of the area of $△$ ABF and the quad. FDCE is -

Q. In a triangle ABC, AB = AC = 20 cm. D, E, F are the midpoints of sides AB, AC and BC respectively. Find the ratio of area of quadrilateral ADFE to the area of triangle ABC .

Q. The altitude from the vertices

A, B

and

C

of the triangle

A B C

meet its circumcircle at

D, E

and

F

respectively. The complex numbers representing the points

D, E and F

are

z_{1}, z_{2} and z_{3}

respectively. If

\frac{z_{3} - z_{1}}{z_{2} - z_{1}}

is purely real, then the triangle

A B C

is right angle at

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90° .

Join BYJU'S Learning Program

In the right angle triangle ∠C=90∘.AE and BD are two medians of a triangle ABC meeting at F. The ratio of the area of △ABF and the quadrilateral FDCE is

In the right angle triangle $∠ C = 90^{\circ} . A E$ and $B D$ are two medians of a triangle $A B C$ meeting at $F$ . The ratio of the area of $△ A B F$ and the quadrilateral $F D C E$ is