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

$\frac{25}{49}$

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$\frac{49}{16}$

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$\frac{36}{49}$

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$\frac{49}{9}$

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Solution

The correct option is C
$\frac{36}{49}$

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

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

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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.
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Trinagles ABC and DEF are similar.
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(ii) If area $(Δ A B C) = 9 c m^{2}, a r e a (Δ D E F) = 64 c m^{2}$ and DE=5.1 cm, find AB.
(iii) If AC = 19 cm adn DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area $(Δ A B C) = 36 c m^{2}$ , are $(Δ D E F) = 64 c m^{2}$ 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 $Δ A B C$ and $Δ D E F$ .

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

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If △ABC∼△ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of △ ABC and △ DEF.

The correct option is C 3649 We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides, area of △ ABCarea of △ DEF=(ABDE)2=(1214)2=3649

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

The correct option is C
$\frac{36}{49}$

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

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