Question : Points $P$ and $Q$ lie on sides $AB$ and $AC$ of triangle $ABC$, respectively, such that segment $PQ$ is parallel to side $BC$. If the ratio of areas of triangle $APQ$ to triangle $ABC$ is 25 : 36, then the ratio of $AP$ to $PB$ is:
Option 1: $5:6$
Option 2: $1:5$
Option 3: $6:5$
Option 4: $5:1$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $5:1$
Solution : We have: $\frac{\text{area of } \Delta APQ}{\text{area of }\Delta ABC}=\frac{25}{36}$ Two triangles $APQ$ and $ABC$ such that $△APQ ∼△ABC$ $⇒\frac{\text{area of }\Delta APQ}{\text{area of }\Delta ABC}=(\frac{AP}{AB})^2$ $⇒\frac{25}{36}=(\frac{AP}{AB})^2$ $⇒\frac{5}{6}=(\frac{AP}{AB})$ If $AB$ = 6 units and $AP$ = 5 units, then $PB = AB - AP$ = 1 unit So, the ratio of $AP:PB$ = $5:1$ Hence, the correct answer is $5:1$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : $D$ and $E$ are points on the sides $AB$ and $AC$ respectively of $\triangle ABC$ such that $DE$ is parallel to $BC$ and $AD: DB = 4:5$, $CD$ and $BE$ intersect each other at $F$. Find the ratio of the areas of $\triangle DEF$ and $\triangle CBF$.
Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE : BC = 6 : 7. (Area of $\triangle {ADE}$ ) : (Area of trapezium BCED) = ?
Question : $D$ and $E$ are points of the sides $AB$ and $AC$, respectively of $\triangle ABC$ such that $DE$ is parallel to $BC$ and $AD:DB=7: 9$. If $CD$ and $BE$ intersect each other at $F$, then find the ratio of areas of $\triangle DEF$ and $\triangle CBF$.
Question : In $\triangle$ABC, D and E are points on AB and AC, respectively, such that DE || BC and DE divide the $\triangle$ABC into two parts of equal areas. The ratio of AD and BD is:
Question : In $\triangle A B C, P$ and $Q$ are points on $AB$ and $BC$, respectively, such that $PQ\parallel AC$. Given that $AB=26, PQ=7$ and $AC=10$, then find the value of $AP$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile