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In the given figure, $DE ‖ BC$ . If $DE = 5 cm, BC = 10 cm$ and $ar (Δ ADE) = 20 c m 2,$ then the area of $△ A B C$ is,

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80 c m 2

40 c m 2

20 c m 2

30 c m 2

answer is A.

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Detailed Solution

Given that DE||BC where DE=5 cm, BC=10cm and ar of △ADE=20

{cm}^{2} .

The ratio of areas of two similar triangles are equal.
Therefore,

a r Δ A D E a r Δ A B C = D E 2 B C 2

On substituting the values,

a r Δ A D E a r Δ A B C = D E 2 B C 2 ⇒ 20 a r Δ A B C = 52102 ⇒ 20 a r Δ A B C = 25100 ⇒ 20 a r Δ A B C = 14

⇒ ar Δ A B C = 420 ⇒ ar Δ A B C = 80 cm 2

Thus, the area of the

ΔABC

80 c m 2 .

Hence, option 1 is correct.

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