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
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{\text{Area of $\Delta \mathrm{ADE}$}}{{\text{Area of $\Delta \mathrm{ABC}$}}}=(\frac{\mathrm{AD}}{\mathrm{AB}})^2$ ⇒ $\frac{\text{Area of $\Delta \mathrm{ADE}$}}{{200}}=(\frac{\mathrm{1}}{\mathrm{5}})^2$ ⇒ $\frac{\text{Area of $\Delta \mathrm{ADE}$}}{{200}}=(\frac{\mathrm{1}}{\mathrm{25}})$ ⇒ $\text{Area of $\Delta \mathrm{ADE}$}=8\;\mathrm{cm^2}$ The area of quadrilateral $\mathrm{DECB}=\text{Area of $\Delta \mathrm{ABC}$}-\text{Area of $\Delta \mathrm{ADE}$}$ $=200\;\mathrm{cm^2}-8\;\mathrm{cm^2}=192\;\mathrm{cm^2}$ Hence, the correct answer is $192$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : Parallel sides of a trapezium are $26\;\mathrm{cm}$ and $40\;\mathrm{cm}$ and the area is $792\;\mathrm{cm^2}$. What is the value of the distance (in $\mathrm{cm}$) between parallel sides?
Question : In $\Delta\mathrm{ ABC,AD}$ and $\mathrm{AE}$ are bisectors of $\angle \mathrm{BAC}$ and $\angle \mathrm{BAD}$ respectively. If $\angle \mathrm{BAE}=30^{\circ}, \mathrm{AE}=9\;\mathrm{cm}$ and $\mathrm{EC}=15\;\mathrm{cm}$, what is the area
Question : For a triangle ABC, D and E are two points on AB and AC such that $\mathrm{AD}=\frac{1}{6} \mathrm{AB}$, $\mathrm{AE}=\frac{1}{6} \mathrm{AC}$. If BC = 22 cm, then DE is _______. (Consider up to two decimals)
Question : In $\triangle \mathrm{ABC}$, AB = AC, and D is a point on side AC such that BD = BC. If AB = 12.5 cm and BC = 5 cm, then what is the measure of DC?
Question : The sides AB, BC, and AC of a $\triangle {ABC}$ are 12 cm, 8 cm, and 10 cm respectively. A circle is inscribed in the triangle touching AB, BC, and AC at D, E, and F respectively. The difference between the lengths of AD and CE is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile