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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

If Δ ABC ∼Δ...

Question

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 $Δ D E F$

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Solution

As we know if two $△ A B C$ and $△ D E F$ are similar-
$\frac{a r e a o f △ A B C}{a r e a o f △ D E F} = \frac{A B^{2}}{D E^{2}}$

$\frac{a r e a o f △ A B C}{a r e a o f △ D E F} = \frac{{1.2}^{2}}{{1.4}^{2}}$

$\frac{a r e a o f △ A B C}{a r e a o f △ D E F} = \frac{1.44}{1.96}$

$\frac{a r e a o f △ A B C}{a r e a o f △ D E F} = \frac{36}{49}$

Hence, ratio of area of $△ A B C$ and $△ D E F$ is $36 : 49.$

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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]

Trinagles ABC and DEF are similar.
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(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.
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