Question : D and E are points on sides AB and AC of $\Delta ABC$. DE is parallel to BC. If AD : DB = 2 : 3. What is the ratio of the area of $\Delta ADE$ and the area of quadrilateral BDEC?
Option 1: 4 : 21
Option 2: 4 : 25
Option 3: 4 : 29
Option 4: 4 : 9
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 4 : 21
Solution : AD : DB = 2 : 3 Let AD =$2x$ DB = $3x$ Now, the ratio of the area of the similar triangle is equal to the square of the ratio of their corresponding sides. Hence, in similar $\triangle ABC$ and $\triangle ADE$ $\frac{\text{Area of}\triangle ABC}{\text{Area of}\triangle ADE}=\frac{AB^2}{AD^2}$ ⇒ $\frac{\text{Area of}\triangle ABC}{\text{Area of}\triangle ADE}=\frac{(5x)^2}{(2x)^2} = \frac{25}{4}$ Let the area of$\triangle ABC$ be 25k and the area of $\triangle ADE$ be 4k $\therefore$ Area of quadrilateral BDEC = Area of $\triangle ABC-$Area of $\triangle ADE$ = 25k – 4k = 21k The ratio of the area of $\Delta ADE$ and the area of quadrilateral BDEC = 4 : 21. Hence, the correct answer is 4 : 21.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : In $\triangle ABC$, $D$ and $E$ are the points of sides $AB$ and $BC$ respectively such that $DE \parallel AC$ and $AD : DB = 3 : 2$. The ratio of the area of trapezium $ACED$ to that of $\triangle DBE$ is:
Question : In $\triangle$ABC, D and E are two points on the sides AB and AC, respectively, so that DE $\parallel$ BC and $\frac{AD}{BD}=\frac{2}{3}$. Then $\frac{\text{Area of trapezium DECB}}{\text{Area of $\triangle$ABC}}$ is equal to:
Question : In a $\triangle ABC$, the median AD, BE, and CF meet at G, then which of the following is true?
Question : If in a $\triangle$ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $\frac{AD}{BD}$ = $\frac{3}{5}$. If AC = 4 cm, then AE is:
Question : In $\Delta ABC$, two points $D$ and $E$ are taken on the lines $AB$ and $BC,$ respectively in such a way that $AC$ is parallel to $DE$. Then $\Delta ABC$ and $\Delta DBE$ are:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile