Question : In the given figure, in $ riangle \operatorname{STU}$, $\mathrm{ST }= 8$ cm, $\mathrm{TU} = 9$ cm and $\mathrm{SU} = 12$ cm. $\mathrm{QU }= 24$ cm, $\mathrm{SR} = 32$ cm and $\mathrm{PT }= 27$ cm. What is the ratio of the area of $ riangle \operatorname{PUQ}$ and the area of $ riangle\operatorname{PTR}$?

Option 1: 1 : 1
Option 2: 4 : 9
Option 3: 2 : 3
Option 4: 5 : 2

Question

Question : In the given figure, in $ riangle \operatorname{STU}$, $\mathrm{ST }= 8$ cm, $\mathrm{TU} = 9$ cm and $\mathrm{SU} = 12$ cm. $\mathrm{QU }= 24$ cm, $\mathrm{SR} = 32$ cm and $\mathrm{PT }= 27$ cm. What is the ratio of the area of $ riangle \operatorname{PUQ}$ and the area of $ riangle\operatorname{PTR}$?

Option 1: 1 : 1

Option 2: 4 : 9

Option 3: 2 : 3

Option 4: 5 : 2

Team Careers360 · Accepted Answer

Correct Answer: 4 : 9

Solution : Using the Sine rule,
In $ riangle \operatorname{PUQ}$,
Area of $ riangle \operatorname{PUQ}=\frac{1}{2}× \sin (\operatorname{\angle PUQ})×\operatorname{PU}×\operatorname{QU}$
⇒ Area of $ riangle \operatorname{PUQ}=\frac{1}{2}× \sin (\operatorname{\angle PUQ})×18×24$
⇒ Area of $ riangle \operatorname{PUQ}=18× \sin (\operatorname{\angle PUQ}) ×12$
In $ riangle \operatorname{PTR}$,
Area of $ riangle \operatorname{PTR}=\frac{1}{2}× \sin (\operatorname{\angle PTR})×\operatorname{PT}×\operatorname{TR}$
⇒ Area of $ riangle \operatorname{PTR}=\frac{1}{2}× \sin (\operatorname{\angle PTR})×27×24$
⇒ Area of $ riangle \operatorname{PTR}=27× \sin (\operatorname{\angle PTR})×12$
In $ riangle \operatorname{SUT}$,
$\frac{1}{2}× \sin \operatorname{(180^{\circ}–\angle PTR)}×8×9=\frac{1}{2}× \sin \operatorname{(180^{\circ}–\angle PUQ)}×12×9$
⇒ $4× \sin (\operatorname{\angle PTR})=6× \sin (\operatorname{\angle PUQ})$
⇒ $\frac{\sin (\operatorname{\angle PTR})}{\sin (\operatorname{\angle PUQ})}=\frac{3}{2}$
$ herefore\frac{\operatorname{Area of riangle PUQ}}{ \operatorname{Area of riangle PTR}}=\frac{18× \sin (\operatorname{\angle PUQ})×12}{27× \sin (\operatorname{\angle PTR})×12}=\frac{2×2}{3×3}=\frac{4}{9}$
Hence, the correct answer is 4 : 9.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Online Courses

Products

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Student Visas

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : In the given figure, in △STU, ST=8 cm, TU=9 cm and SU=12 cm. QU=24 cm, SR=32 cm and PT=27 cm. What is the ratio of the area of △PUQ and the area of △PTR? Option 1: 1 : 1Option 2: 4 : 9Option 3: 2 : 3Option 4: 5 : 2

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : In the given figure, in $△ STU$ , $ST = 8$ cm, $TU = 9$ cm and $SU = 12$ cm. $QU = 24$ cm, $SR = 32$ cm and $PT = 27$ cm. What is the ratio of the area of $△ PUQ$ and the area of $△ PTR$ ?

Option 1: 1 : 1
Option 2: 4 : 9
Option 3: 2 : 3
Option 4: 5 : 2