Question

3.In the figure AD=4cm,BD=2cm.If area of triangle ADC=20 sq.cm,what is the area of triangle BDC ?​

Answer 1

Answer:

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

$\boxed{ \sf \: Then , \dfrac{ar\ (ABC)}{ar\ (ADE)}=\dfrac{AB^2}{AD^2}}$

[ ∵ The ratio area of similar triangles is equal to the ratio of the square of two corresponding sides. ]

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

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

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

Answer 2

Step-by-step explanation:

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