Question

In given figure ,DE //BC .if AD =4cm and DB =2cm ,find the area of ABC if area of ADE =16cm^2​

Answer 1

Answer:

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Answer 2

The area of triangle ABC  is 36 sq. cm.

Explanation:

Given : In  Δ ABC, DE || BC

AD =4cm and DB =2cm

Then , AB = AD+DB= 4+2= 6 cm

In   Δ ABC and  ΔADE , we have

∠A=∠A

∠ADE= ∠ABC   [corresponding angles ]

∴ BY AA-similarity criteria

Δ ABC≈  ΔADE

Then , $\dfrac{ar\ (ABC)}{ar\ (ADE)}=\dfrac{AB^2}{AD^2}$  [ ∵ The ratio area of similar triangles is equal to the ratio of the square of two corresponding sides. ]

$\dfrac{ar(ABC)}{16}=\dfrac{(6)^2}{4^2}$

$ar (ABC) =\dfrac{36}{16}\times16=36\ cm^2$

Hence, the area of triangle ABC  is 36 sq. cm.

# Learn more :

In a triangle ABC,DE||BC, AD=2CM and DB=4CM then AE:AC==

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