Question

D and E are midpoints of sides AB and AC respectively. ar(DECB) = 6A then ar(ABC) is equal to:

Answer 1

Answer:

12A

Step-by-step explanation:

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Answer 2

Answer:

D and E are midpoints of sides AB and AC respectively. ar(DECB) = 6A then ar(ABC) is equal to-

Solution:

Understand that,

Area of ABC = Area of ADE+ Area of BDEC

Use mid point theorem,

$\[ \Rightarrow \frac{{A{E^2}}}{{A{C^2}}} = \frac{{Ar.\left( {ADE} \right)}}{{Ar.\left( {ABE} \right)}}\]$

$\[ \Rightarrow \frac{1}{{{2^2}}} = \frac{{Ar.\left( {ABC} \right) - Ar.\left( {DECB} \right)}}{{Ar.\left( {ABC} \right)}}\]$

$\[ \Rightarrow \frac{1}{4} = \frac{{Ar.\left( {ABE} \right) - 6A}}{{Ar.\left( {ABC} \right)}}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow Ar.\left( {ABC} \right) = 4Ar.\left( {ABC} \right) - 24A\\ \Rightarrow 3Ar.\left( {ABC} \right) = 24A\\ \Rightarrow Ar.\left( {ABC} \right) = 8A\end{array}\]$

Hence, the area of the triangle ABC is 8A.