ABC - DEF - If BC - 3 cm- EF - 4 cm and arABC - 54 cm2 - then arDEF -

The correct option is A 96 cm^2 For similar triangles #160; (BCEF)^2=ArΔ ABCArΔ DEF ( 34)^2=54ArΔ DEF Ar(Δ DEF)=54×169=96cm^2 ...

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Byju's Answer

Standard IX

Mathematics

If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

ABC ∼ DEF ....

Question

ABC $\sim$ DEF . If BC = 3 cm, EF = 4 cm and ar(ABC) = 54 $c m^{2}$ , then ar(DEF) =

108

c m^{2}

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c m^{2}

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c m^{2}

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100

c m^{2}

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Solution

The correct option is A 96 $c m^{2}$
For similar triangles
${(\frac{B C}{E F})}^{2} = \frac{A r Δ A B C}{A r Δ D E F} {(\frac{3}{4})}^{2} = \frac{54}{A r Δ D E F} A r (Δ D E F) = 54 \times \frac{16}{9} = 96 c m^{2}$

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Similar questions

In the given figure, $△ A B C$ and $△ D E F$ are similar. If BC = 3 cm, EF = 4 cm and area of $△ A B C$ is 54 cm $^{2}$ , then the area of $△ D E F$ is _____ cm $^{2}$ .

Q. If

△ A B C

is similar to

△ D E F

such that BC=3 cm, EF=4 cm and area of

△ A B C = 54 {c m}^{2}

. Determine the area of

△ D E F

Q. In

△ A B C \sim △ D E F

, BC

=

4 cm, EF

=

5 cm and area(

△

ABC)

=

c m^{2}

, the area(

△

DEF) is:

Q. Triangles ABC and DEF are similar.

(i) If area (

△ A B C

)= 16

{cm}^{2}

, area(

△

DEF)= 25

{cm}^{2}

and

B C = 2.3 cm

, find

E F

(ii) If area (

△ A B C

)= 9

{cm}^{2}

, area(

△

DEF) = 64

{cm}^{2}

and

D E = 5.1 cm

, find

A B

(iii) If

A C = 19 cm

and

D F = 8 cm

, find ratio of the area of two triangles.

(iv) If area (

△ A B C

)= 36

{cm}^{2}

, area (

△

DEF) =64

{cm}^{2}

and

D E = 6.2 cm

, find

A B

(v) If

A B = 1.2 cm

and

D E = 1.4 cm

, find the ratio of the areas of triangle

A B C

and

D E F

Q. Let

Δ A B C \sim △ D E F

and their areas be, respectively.resp2ctively, 64

{c m}^{2}

and 121

{c m}^{2}

. If EF =

15.4 c m,

find

B C

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ABC ∼ DEF . If BC = 3 cm, EF = 4 cm and ar(ABC) = 54 cm2 , then ar(DEF) =

The correct option is A 96 cm2For similar triangles (BCEF)2=ArΔABCArΔDEF(34)2=54ArΔDEFAr(ΔDEF)=54×169=96cm2

ABC $\sim$ DEF . If BC = 3 cm, EF = 4 cm and ar(ABC) = 54 $c m^{2}$ , then ar(DEF) =

The correct option is A 96 $c m^{2}$
For similar triangles
${(\frac{B C}{E F})}^{2} = \frac{A r Δ A B C}{A r Δ D E F} {(\frac{3}{4})}^{2} = \frac{54}{A r Δ D E F} A r (Δ D E F) = 54 \times \frac{16}{9} = 96 c m^{2}$