Question : In $\Delta \mathrm{ABC}$, a line parallel to side $\mathrm{BC}$ cuts the sides $\mathrm{AB}$ and $\mathrm{AC}$ at points $\mathrm{D}$ and $\mathrm{E}$ respectively and also point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio of $\mathrm{1 : 4}$. If the area of $\Delta \mathrm{ABC}$ is $200\;\mathrm{cm^2}$, then what is the area (in $\mathrm{cm^2}$) of quadrilateral $\mathrm{DECB}$?
Option 1: 192
Option 2: 50
Option 3: 120
Option 4: 96

Question

Question : In $\Delta \mathrm{ABC}$, a line parallel to side $\mathrm{BC}$ cuts the sides $\mathrm{AB}$ and $\mathrm{AC}$ at points $\mathrm{D}$ and $\mathrm{E}$ respectively and also point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio of $\mathrm{1 : 4}$. If the area of $\Delta \mathrm{ABC}$ is $200\;\mathrm{cm^2}$, then what is the area (in $\mathrm{cm^2}$) of quadrilateral $\mathrm{DECB}$?

Option 1: 192

Option 2: 50

Option 3: 120

Option 4: 96

Team Careers360 · Accepted Answer

Correct Answer: 192

Solution :
Given: $\mathrm{AD:DB=1:4}$ and the area of $\Delta \mathrm{ABC}$ is $200\;\mathrm{cm^2}$.
In $\Delta \mathrm{ABC}$,
$\mathrm{DE}\parallel\mathrm{BC}$
So, $\Delta \mathrm{ADE}\sim\Delta \mathrm{ABC}$,
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
⇒ $\frac{ ext{Area of $\Delta \mathrm{ADE}$}}{{ ext{Area of $\Delta \mathrm{ABC}$}}}=(\frac{\mathrm{AD}}{\mathrm{AB}})^2$
⇒ $\frac{ ext{Area of $\Delta \mathrm{ADE}$}}{{200}}=(\frac{\mathrm{1}}{\mathrm{5}})^2$
⇒ $\frac{ ext{Area of $\Delta \mathrm{ADE}$}}{{200}}=(\frac{\mathrm{1}}{\mathrm{25}})$
⇒ $ ext{Area of $\Delta \mathrm{ADE}$}=8\;\mathrm{cm^2}$
The area of quadrilateral $\mathrm{DECB}= ext{Area of $\Delta \mathrm{ABC}$}- ext{Area of $\Delta \mathrm{ADE}$}$
$=200\;\mathrm{cm^2}-8\;\mathrm{cm^2}=192\;\mathrm{cm^2}$
Hence, the correct answer is $192$.

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Question : In ΔABC, a line parallel to side BC cuts the sides AB and AC at points D and E respectively and also point D divides AB in the ratio of 1:4. If the area of ΔABC is 200cm2, then what is the area (in cm2) of quadrilateral DECB?Option 1: 192Option 2: 50Option 3: 120Option 4: 96

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