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Standard X

Mathematics

Relation between Area and Sides of Similar Triangles

If Δ ABC ∼ ...

Question

If $Δ A B C \sim D E F$ , $A B : D E = 3 : 4$ , then find the ratio of area of triangles. If $A B C - D E F, A B : D E = 3 : 4$ , then find the ratio of area of triangles.

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Solution

Given that:
$△ A B C \sim △ D E F$ and $A B : D E = 3 : 4$
By properties of similar triangles,
$\frac{a r (△ A B C)}{a r (△ D E F)} = \frac{A B^{2}}{D E^{2}}$
$\Rightarrow \frac{a r (△ A B C)}{a r (△ D E F)} = \frac{A B^{2}}{D E^{2}} = \frac{3^{2}}{4^{2}} = \frac{9}{16}$

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Similar questions

A X

and

D Y

are altitiudes of two triangles

△ A B C

and

△ D E F

. Prove that

A X : D Y = A B : D E

If $△$ ABC ~ $△$ DEF such that AB = 1.2 cm and DE = 1.4 cm . Find the ratio of area of $△$ ABC and $△$ DEF.

Q. Triangles

A B C

and

D E F

are similar.

(i) If area (

△

ABC)=

16

c m^{2}

, area(

△

DEF)=

25

c m^{2}

and BC =

2.34

cm, find EF.

(ii) If area (

△

ABC)=

9

c m^{2}

, area(

△

DEF) =

64

c m^{2}

and DE=

5.1

cm, find AB.

(iii) If AC =

19

cm and DF=

8

cm, ratio of the area of two triangles.

(iv) If area (

△

ABC)=

36

c m^{2}

, area (

△

DEF) =

64

c m^{2}

and DE=

6.2

cm, find AB.

(v) If AB=

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1.4

find the ratio of the areas of triangle ABC and DEF.

Q. If ∆ABC and ∆DEF are two triangles such that

\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{2}{5}

, then Area (∆ABC) : Area (∆DEF) =

(a) 2 : 5
(b) 4 : 25
(c) 4 : 15
(d) 8 : 125

Q. ABC

~

DEF
If AB= 2.4 cm and DE= 1.6 cm, find the ratio of the areas of

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If ΔABC∼DEF, AB:DE=3:4, then find the ratio of area of triangles. If ABC−DEF,AB:DE=3:4, then find the ratio of area of triangles.

Given that:△ABC∼△DEF and AB:DE=3:4By properties of similar triangles,ar(△ABC)ar(△DEF)=AB2DE2⇒ar(△ABC)ar(△DEF)=AB2DE2=3242=916

If $Δ A B C \sim D E F$ , $A B : D E = 3 : 4$ , then find the ratio of area of triangles. If $A B C - D E F, A B : D E = 3 : 4$ , then find the ratio of area of triangles.

Given that:
$△ A B C \sim △ D E F$ and $A B : D E = 3 : 4$
By properties of similar triangles,
$\frac{a r (△ A B C)}{a r (△ D E F)} = \frac{A B^{2}}{D E^{2}}$
$\Rightarrow \frac{a r (△ A B C)}{a r (△ D E F)} = \frac{A B^{2}}{D E^{2}} = \frac{3^{2}}{4^{2}} = \frac{9}{16}$