Question : ABCD is a square. Draw a triangle QBC on side BC considering BC as a base and draw a triangle PAC on AC as its base such that $\Delta$QBC$\sim\Delta$PAC. Then, $\frac{\text{Area of $\Delta$QBC}}{\text{Area of $\Delta$PAC}}$ is equal to:
Option 1: $\frac{1}{2}$
Option 2: $\frac{2}{1}$
Option 3: $\frac{1}{3}$
Option 4: $\frac{2}{3}$
New: SSC CHSL Tier 2 answer key released | 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: $\frac{1}{2}$
Solution : We have, $\Delta$QBC$\sim\Delta$PAC Since ABCD is a square, AB = BC = CD = DA In $\Delta$ABC, $ ⇒AC=\sqrt{(AB)^2+(BC)^2}$ $⇒ AC=\sqrt{(2BC)^2}$ $⇒AC=\sqrt{2}BC$ In similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. $⇒\frac{\text{Area of $\Delta$QBC}}{\text{Area of $\Delta$PAC}}=(\frac{BC}{AC})^2$ $⇒\frac{\text{Area of $\Delta$QBC}}{\text{Area of $\Delta$PAC}}=(\frac{BC}{\sqrt{2}BC})^2$ $⇒\frac{\text{Area of $\Delta$QBC}}{\text{Area of $\Delta$PAC}}=\frac{1}{2}$ Hence, the correct answer is $\frac{1}{2}$.
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 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 triangle RST, M and N are two points on RS and RT such that MN is parallel to the base ST of the triangle RST. If $\text{RM}=\frac{1}{3} \text{MS}$ and $\text{ST}=5.6 \text{ cm}$, what is the ratio of
Question : If $\frac{xy}{x+y}=a$, $\frac{xz}{x+z}=b$ and $\frac{yz}{y+z}=c$, where $a,b,c$ are all non-zero numbers, $x$ equals to:
Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:
Question : $\triangle A B C$ inscribe in a circle with centre O. If AB = 9 cm, BC = 40 cm, and AC = 41 cm, then what is the circum-radius of the triangle?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile