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Standard X

Mathematics

Relation between Area and Sides of Similar Triangles

If ABC ∼ DEF ...

Question

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

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Solution

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

∴ $\frac{A r e a (△ A B C)}{A r e a (△ D E F)} = \frac{A B^{2}}{D F^{2}}$

$\Rightarrow$ $\frac{A r e a (△ A B C)}{A r e a (△ D E F)} = {(\frac{12}{14})}^{2} = \frac{(1.2)^{2}}{(1.4)^{2}}$ = $\frac{36}{49}$

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Similar questions

Q. In

△ A B C \sim △ D E F

such that

A B = 1.2 c m

and

D E = 1.4 c m

. Find the ratio of areas of

△ A B C

and

△ D E F

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

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(ii) If area (

△ A B C

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, area(

△

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and

D E = 5.1 cm

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A B

(iii) If

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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

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(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

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Q. If

△ A B C \sim △ D E F

such that AB=1.2 cm and DE=1.4 cm. Find the ratio of areas of

△ A B C

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△ D E F

If $△ A B C \sim △$ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of $△$ ABC and $△$ DEF.

Q. Triangles ABC and DEF are similar.

(i) If area (∆ABC) = 16 cm², area (∆DEF) = 25 cm² and BC = 2.3 cm, find EF.
(ii) If area (∆ABC) = 9 cm², area (∆DEF) = 64 cm² and DE = 5.1 cm , find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² and DE = 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF.

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

We know that the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. ∴ Area (△ABC)Area (△DEF)=AB2DF2 ⇒ Area (△ABC)Area (△DEF)=(1214)2=(1.2)2(1.4)2 = 3649

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