Question : If $D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD: DB = 2:3$ and the area of $\Delta ADE$ is 4 sq. cm, what is the area (in sq. cm) of quadrilateral $BDEC$?
Option 1: 25
Option 2: 21
Option 3: 5
Option 4: 9

Question

Question : If $D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD: DB = 2:3$ and the area of $\Delta ADE$ is 4 sq. cm, what is the area (in sq. cm) of quadrilateral $BDEC$?

Option 1: 25

Option 2: 21

Option 3: 5

Option 4: 9

Team Careers360 · Accepted Answer

Correct Answer: 21

Solution :
We have,
$AD:DB = 2:3$, area($ riangle ADE$) = 4 sq. cm
Let $AD = 2x$ and $DB = 3x$
So, $AB = AD + DB = 2x + 3x = 5x$
Two triangles $ABC$ and $ADE$ such that $ riangle ABC$ ∼$ riangle ADE$
So, $\frac{ ext{area of} ( riangle ABC)}{ ext{area of } ( riangle ADE)}=(\frac{AB}{AD})^2$
⇒ $\frac{ ext{area of} ( riangle ABC)}{4}=(\frac{5x}{2x})^2$
⇒ $\frac{ ext{area of} ( riangle ABC)}{4}=\frac{25}{4}$
⇒ area of ($ riangle ABC$) = 25 sq. cm
Area of quadrilateral $BDEC$ = area of ($ riangle ABC$)–area of ($ riangle ADE$) = 25 – 4 = 21 sq.cm
Hence, the correct answer is 21.

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Question : If D and E are points on sides AB and AC of ΔABC. DE is parallel to BC. If AD:DB=2:3 and the area of ΔADE is 4 sq. cm, what is the area (in sq. cm) of quadrilateral BDEC?Option 1: 25Option 2: 21Option 3: 5Option 4: 9

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Question : If $D$ and $E$ are points on sides $A B$ and $A C$ of $Δ A B C$ . $D E$ is parallel to $B C$ . If $A D : D B = 2 : 3$ and the area of $Δ A D E$ is 4 sq. cm, what is the area (in sq. cm) of quadrilateral $B D E C$ ?
Option 1: 25
Option 2: 21
Option 3: 5
Option 4: 9