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Q.

In the given figure, $Δ ABC ~ Δ ADE$ and $DE | | BC$ . If DE=3cm, BC=6cm and area $(Δ ADE) = 15$ ${cm}^{2},$ then the area of $Δ ABC$ is ____ ${cm}^{2}$ .

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Detailed Solution

Δ ABC ~ Δ ADE

and

DE | | BC

. If DE=3cm , BC=6cm and area

(Δ ADE) = 15

{cm}^{2}

, then the area of

Δ ABC

is 60

{cm}^{2}

.
Given triangle is,
Question Image

Question Image

The ratio of area of two similar triangles is equal to square of the ratio of their corresponding sides.
As given, the triangles ΔABC and ΔADE are similar, their ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides,

\Rightarrow \frac{ar (ΔADE)}{ar (ΔABC)} = \frac{{AD}^{2}^{}}{{AB}^{2}^{}} = \frac{{AE}^{2}^{}}{{AC}^{2}^{}} = \frac{{DE}^{2}^{}}{{BC}^{2}^{}}

Therefore,

a r Δ ADE a r Δ ABC = DE 2 BC 2 ⇒ 15 a r Δ ABC = 3262 ⇒ 15 a r Δ ABC = 936 ⇒ a r Δ ABC = 60 cm 2

So, the area of the triangle

Δ

ABC is 60

{cm}^{2}

.

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