Question : In $\triangle \mathrm{ABC}$, $AB=20$ cm, $BC=7$ cm and $CA=15$ cm. Side $BC$ is produced to $D$ such that $\triangle \mathrm{DAB} \sim \triangle \mathrm{DCA}$. $DC$ is equal to:
Option 1: 9 cm
Option 2: 8 cm
Option 3: 10 cm
Option 4: 7 cm
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: 9 cm
Solution : Given: AB = 20 cm BC = 7 cm CA = 15 cm and $\triangle DAB\sim\triangle DCA$ Let $CD\ =\ x$ and $AD\ =\ y$ Since $\triangle DAB\sim\triangle DCA$ ⇒ $\frac{AB}{AC}\ =\ \frac{DB}{AD}\ =\ \frac{AD}{DC}$ Take the first two parts of the equation, we get $\Rightarrow \frac{20}{15}\ =\ \frac{7\ +\ x}{y}$ $\Rightarrow \frac{4}{3}\ =\ \frac{7\ +\ x}{y}$ $\Rightarrow y\ =\ \frac{21\ +\ 3x}{4}$..................(1) Take the first and third part $\Rightarrow \frac{y}{x}\ =\ \frac{4}{3}$ $\Rightarrow y\ =\ \frac{4x}{3}$........... (2) from equation (1) and (2) $\Rightarrow \frac{21\ +\ 3x}{4}\ =\ \frac{4x}{3}$ $\Rightarrow 16x\ =\ 63\ + 9x$ $\Rightarrow 7x\ =\ 63$ $\Rightarrow x\ =\ 9$ So, the length of DC is 9 cm. Hence, the correct answer is 9 cm.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : If $\triangle A B C \sim \triangle F D E$ such that $A B=9 \mathrm{~cm}, A C=11 \mathrm{~cm}, D F=16 \mathrm{~cm}$ and $D E=12 \mathrm{~cm}$, then the length of $BC$ is:
Question : If $\triangle ABC \sim \triangle QRP, \frac{\operatorname{area}(\triangle A B C)}{\operatorname{area}(\triangle Q R P)}=\frac{9}{4}, A B=18 \mathrm{~cm}, \mathrm{BC}=15 \mathrm{~cm}$, then the length of $\mathrm{PR}$ is:
Question : In a $\triangle ABC$, if $\angle A=90^{\circ}, AC=5 \mathrm{~cm}, BC=9 \mathrm{~cm}$ and in $\triangle PQR, \angle P=90^{\circ}, PR=3 \mathrm{~cm}, QR=8$ $\mathrm{cm}$, then:
Question : $\triangle ABC$ is an isosceles triangle with AB = AC = 15 cm and an altitude from A to BC of 12 cm. The length of side BC is:
Question : In an equilateral triangle ABC, D is the midpoint of side BC. If the length of BC is 8 cm, then the height of the triangle is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile