Q. 164.3( 12 Votes )

# If D, E, F are the mid-points of sides BC, CA and AB respectively of A ABC, then the ratio of the areas of triangles DEF and ABC is

A. 1 :4

B. 1 : 2

C. 2 : 3

D. 4 : 5

Answer :

Given D, E and F are the mid-points of sides BC, CA and AB respectively of ΔABC.

Then DE || AB, DE || FA … (1)

And DF || CA, DF || AE … (2)

From (1) and (2), we get AFDE is a parallelogram.

Similarly, BDEF is a parallelogram.

In ΔADE and ΔABC,

⇒ ∠FDE = ∠A [Opposite angles of ||gm AFDE]

⇒ ∠DEF = ∠B [Opposite angles of ||gm BDEF]

∴ By AA similarity criterion, ΔABC ~ ΔDEF.

We know that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

∴ ar (ΔDEF): ar (ΔABC) = 1: 4

Rate this question :

, ar () = 9 cm^{2}, ar () = 16 cm^{2}. If BC = 2.1 cm, then the measure of EF is

. such that ar () = 4 ar (). If BC =12 cm, then QR =

RD Sharma - MathematicsIf and are two triangles such that , then Area (): Area () =

RD Sharma - MathematicsThe areas of two similar triangles are in respectively 9 cm^{2} and 16 cm^{2}. The ratio of their corresponding sides is

The areas of two similar triangles and are 144 cm^{2} and 81 cm^{2} respectively. If the longest side of larger A ABC be 36 cm, then. the longest side of the smaller triangle is

In Fig. 4.236, and AP : PB = 1 : 2. Find [CBSE 2008]

RD Sharma - Mathematics

If and are two triangles such that , then write Area (): Area ().

RD Sharma - Mathematics