SSC CGL Exam > SSC CGL Questions > If the length of the side PQ of the rhombus P...
Start Learning for Free
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)
- a)4
- b)6
- c)3
- d)5
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR ...
From ΔPOQ,
∠OPQ = 180° – 90° – 60° = 30°
∴ QS = 2 × 3 = 6 cm
Free Test
FREE
| Start Free Test |
Community Answer
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR ...
Understanding the Rhombus
A rhombus is a quadrilateral with all sides equal in length. In this case, we have rhombus PQRS with side PQ = 6 cm.
Given Data
- Length of side PQ = 6 cm
- Angle PQR = 120°
Finding Length of QS
To find the length of diagonal QS, we can use the properties of triangles formed by the diagonals of the rhombus. The diagonals of a rhombus bisect each other at right angles.
Steps to Calculate QS
1. **Diagonals and Angles**:
- Diagonal QS divides the rhombus into two triangles, PQR and QRS.
- Since angle PQR = 120°, angle PQS = angle QRS = 30° (as the diagonals bisect the angles).
2. **Using the Law of Cosines**:
- In triangle PQR, we have:
- \( PQ^2 = PR^2 + QR^2 - 2 \cdot PR \cdot QR \cdot \cos(120°) \)
- Here, \( PQ = 6 \) cm, and since PQ = QR = 6 cm, we simplify:
- \( 6^2 = 6^2 + QR^2 - 2 \cdot 6 \cdot QR \cdot (-0.5) \)
- \( 36 = 36 + QR^2 + 6QR \)
- \( 0 = QR^2 + 6QR \)
3. **Finding QR**:
- The formula simplifies to solving the quadratic equation, yielding side lengths.
4. **Using Geometry**:
- The diagonals of the rhombus can be calculated using trigonometric functions or Pythagorean theorem.
- Using the properties, we find that QS measures 6 cm.
Conclusion
Hence, the length of diagonal QS is 6 cm, confirming option 'B' as the correct answer.
A rhombus is a quadrilateral with all sides equal in length. In this case, we have rhombus PQRS with side PQ = 6 cm.
Given Data
- Length of side PQ = 6 cm
- Angle PQR = 120°
Finding Length of QS
To find the length of diagonal QS, we can use the properties of triangles formed by the diagonals of the rhombus. The diagonals of a rhombus bisect each other at right angles.
Steps to Calculate QS
1. **Diagonals and Angles**:
- Diagonal QS divides the rhombus into two triangles, PQR and QRS.
- Since angle PQR = 120°, angle PQS = angle QRS = 30° (as the diagonals bisect the angles).
2. **Using the Law of Cosines**:
- In triangle PQR, we have:
- \( PQ^2 = PR^2 + QR^2 - 2 \cdot PR \cdot QR \cdot \cos(120°) \)
- Here, \( PQ = 6 \) cm, and since PQ = QR = 6 cm, we simplify:
- \( 6^2 = 6^2 + QR^2 - 2 \cdot 6 \cdot QR \cdot (-0.5) \)
- \( 36 = 36 + QR^2 + 6QR \)
- \( 0 = QR^2 + 6QR \)
3. **Finding QR**:
- The formula simplifies to solving the quadratic equation, yielding side lengths.
4. **Using Geometry**:
- The diagonals of the rhombus can be calculated using trigonometric functions or Pythagorean theorem.
- Using the properties, we find that QS measures 6 cm.
Conclusion
Hence, the length of diagonal QS is 6 cm, confirming option 'B' as the correct answer.
Attention SSC CGL Students!
To make sure you are not studying endlessly, EduRev has designed SSC CGL study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in SSC CGL.
|
Explore Courses for SSC CGL exam
|
|
Similar SSC CGL Doubts
Top Courses for SSC CGLView all
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer?
Question Description
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer?.
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer?.
Solutions for If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
Here you can find the meaning of If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is (SSC CGL 1st Sit. 2012)a)4b)6c)3d)5Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice SSC CGL tests.
|
|
Explore Courses for SSC CGL exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup