If - ABC - DEF such that AB -1-2 cm and DE -1-4 cm- Find the ratio of area of - ABC and - DEF- -4 MARKS-

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Standard X

Mathematics

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If Δ ABC ∼Δ D...

Question

If $Δ A B C \sim Δ D E F$ such that AB = 1.2 cm and DE = 1.4 cm . Find the ratio of area of $Δ A B C$ and $Δ D E F$ . [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

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

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

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

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Similar questions

Trinagles ABC and DEF are similar.
(i) If area $(Δ A B C) = 16 c m^{2}, a r e a (Δ D E F) = 25 c m^{2}$ and BC = 2.3 cm find EF.
(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 $Δ A B C \sim Δ D E F$ such that $A B = 1.2$ cm and
$D E = 1.4$ cm. Find the ratio of of areas of $Δ A B C$ and $Δ D E F$

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.

If $Δ A B C$ is similar to $Δ D E F$ such that BC = 3 cm, EF = 4 cm and area of $Δ A B C = 54 {c m}^{2}$ . Determine the area of $Δ D E F$ . [4 MARKS]

If $Δ A B C \sim Δ D E F$ such that area of $Δ A B C$ is $9 c m^{2}$ and the area of $Δ D E F$ is $16 c m^{2}$ and BC = 2.1 cm. Find the length of EF. [2 MARKS]

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If ΔABC∼ΔDEF such that AB = 1.2 cm and DE = 1.4 cm . Find the ratio of area of ΔABC and ΔDEF. [4 MARKS]

Concept: 1 Mark Application: 3 Marks 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 (ΔABC)Area (ΔDEF)=AB2DF2 ⇒Area (ΔABC)Area (ΔDEF)=(1214)2=(1.2)2(1.4)2=3649

If $Δ A B C \sim Δ D E F$ such that AB = 1.2 cm and DE = 1.4 cm . Find the ratio of area of $Δ A B C$ and $Δ D E F$ . [4 MARKS]