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In the given figure, ΔABC∿ ΔDEF. If AB = 2DE and area of ΔABC is 56 sq. cm, the area of ΔDEF is[[1]] cm $2$

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Detailed Solution

In the given figure, ΔABC∿ΔDEF. If AB = 2DE and area of ΔABC is 56

c m^{2}

, the area of ΔDEF is 14 cm

.
In the given figure, ΔABC∿ΔDEF, AB = 2DE and area of ΔABC is 56

c m^{2}

The ratio of the areas of two similar triangles equals the ratio of the corresponding sides of the triangle.
Then,

ar Δ A B C ar Δ D E F = A B 2 D E 2

Here, AB and DE are the corresponding sides of the two similar triangles.

ar Δ A B C ar Δ D E F = A B 2 D E 2 ⇒ 56 ar Δ D E F = 2 D E 2 D E 2 ⇒ 56 ar Δ D E F = 4 D E 2 D E 2

⇒ 56 ar Δ D E F = 4 ⇒ ar Δ D E F = 564 ⇒ ar Δ D E F = 14 cm 2

The area of the triangle DEF is

14 c m 2 .

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