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If ΔABC~ΔDEF, AB =10 cm, area (ΔABC) = 20 sq. cm, area (ΔDEF) = 45 sq. cm, then the value of DE is,

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10cm

15cm

20cm

25cm

answer is B.

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Detailed Solution

Given that,
ΔABC~ΔDEF where AB =10 cm, area (ΔABC) = 20 sq. cm and area (ΔDEF) = 45 sq. cm.
Question Image

Δ A B C ~ Δ D E F

, then

A B D E = B C E F = A C D F

Using similarity property in triangles

Δ A B C

and

Δ D E F

a r A B C a r D E F = A B 2 D E 2

......(1)

⇒ 2045 = 102 D E 2 ⇒ 2045 = 100 D E 2 ⇒ D E 2 = 100 × 45 20 ⇒ D E 2 = 225

⇒ D E = 225 ⇒ D E = 15 c m

Therefore, the value of DE is 15cm.
Hence option 2 is correct.

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